Trigonometry

Problem 601

10. Find the exact value of $\cos I$ in simplest radical form.

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Problem 602

Find the exact value of $\tan O$ in simplest radical form.

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Problem 603

Question 36, *5.5.89 HW Score: 88.16\% points Points: 0 of 1
Use a calculator to solve the equation on the interval $[0,2 \pi)$ . $\boldsymbol{\operatorname { t a n }} x=-8$
What are the solutions in the interval $[0,2 \pi)$ ? Select the correct choice below and, if necessary, fil choice. A. $x=$ $\square$ (Type your answer in radians. Round to four decimal places as needed. Use a comma to B. There is no solution.

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Problem 604

Question 38, *5.5.85 HW Score: $93.42 \%, 3$ points
Use a calculator to solve the equation on the interval $[0,2 \pi)$ . Points: 0 of 1 $\sin x=-0.402$
What are the solutions in the interval $[0,2 \pi)$ ? Select the correct choice below and, if necessary, fill choice. A. $x=$ $\square$ (Type your answer in radians. Round to four decimal places as needed. Use a comma to B. There is no solution.

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Problem 605

Rewrite each expression as a single trigonometric ratio, and then evaluate the ratio. a) $\frac{\tan 170^{\circ}-\tan 110^{\circ}}{1+\tan 170^{\circ} \tan 110^{\circ}}$

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Problem 606

1. (13 points) Simplify the trigonometric expression by writing the expression in terms of sines and cosines initially and then simplifying. Your final answer should contain no quotients and be expressed as a single trigonometric function of $\theta$ only. $\frac{\cos \theta}{1-\sin \theta}-\sec \theta$

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Problem 607

The right triangle below has acute angle alpha $(\alpha)$ .
Using this triangle, which of the below are true? $\sin \alpha=\frac{8}{17}$ $\sin \alpha=\frac{15}{17}$ $\cos \alpha=\frac{15}{17}$ $\cos \alpha=\frac{8}{17}$

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Problem 608

Find an equation for the sine graph, $f(x)$ :
Write your answer in the form $\mathrm{f}(\mathrm{x})=$ $\mathrm{A} \sin (\mathrm{Bx}+\mathrm{C})+\mathrm{D}$ , where $\mathrm{A}, \mathrm{B}, \mathrm{C}$ , and D are real numbers. $f(x)=$ $\square$

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Problem 609

Question Show Examples
In $\triangle \mathrm{HIJ}, i=40 \mathrm{~cm}, h=45 \mathrm{~cm}$ and $\angle \mathrm{H}=112^{\circ}$ . Find all possible values of $\angle \mathrm{I}$ , to the nearest 10th of $a$ degree.
Answer Attempt 1 out of 2

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Problem 610

Graph the following function: $y=\csc \left(\frac{1}{2}\left(x-\frac{\pi}{4}\right)\right)-1$
Drag the movable red point to shift the function, the black point to set the vertical asymptotes, and the blue point at the correct set of coordinates. You may click on a point to verify its coordinates.
Note: Make sure to move the points in the direction of the phase shift represented in the function.
Provide your answer below:

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Problem 611

Match each trigonometric function with its derivative by entering the correct letter in the gi A. $y=\tan (7 x)$ B. $y=\tan \left(x^{7}\right)$ $\frac{d y}{d x}=\sec ^{2}\left(x^{7}\right)$ C. $y=\cot ^{7}(x)$ $\frac{d y}{d x}=-7 \cot ^{6}(x) \csc (x)$ $\frac{d y}{d x}=7 x^{6} \sec ^{2}\left(x^{7}\right)$ D. $y=7 \cot (x)$ $\frac{d y}{d x}=-7 \cot ^{6}(x) \csc ^{2}(x)$ E. Not the derivative of $A, B, C$ , or $D$ . $\begin{array}{l} \frac{d y}{d x}=-7 \csc ^{2}(x) \\ \frac{d y}{d x}=7 \sec ^{2}(7 x) \end{array}$

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Problem 612

Part 1 of 3
Write the ratios for $\sin M, \cos M$ , and $\tan M$ .

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Problem 613

19-34 - Amplitude and Period of the function, and sketch its grap
19. $y=\cos 2 x$

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Problem 614

Find the measure of side c .

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Problem 615

Find the value of $x$ .

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Problem 616

Question 1
There are many trig identities. They allow you to solve (trig) equations by hand, and are helpful with calculus.
Below is (the left side of) one trig identity. Using the reading in textbook sections $7.1{ }^{[3}, 7.2 \mathrm{Cl}^{3}$ , and 7.3 (or other links below), identify this formula and type the other side of the identity in the empty box. $\cos (x) \cos (y)-\sin (y) \sin (x)=$

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Problem 617

tower?
61. Elevation of a Kite A tourist is lying on the beach, flying a kite. The tourist holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be $50^{\circ}$ . If the string is 450 ft long, how high is the kite above the ground?

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Problem 618

Use a calculator to approximate the function values in both radians and degrees to 4 decimal places.
Part: $0 / 3$
Part 1 of 3 $\arctan 29 \approx \square \mathrm{rad} \approx \square^{\circ}$

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Problem 619

33-40 ■ Value of an Expression expression.
33. $\cos \left(\sin ^{-1}\left(\frac{4}{5}\right)\right)$

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Problem 620

Use a calculator to approximate the function values in both radians and degrees to 4 decimal places.
Part: $0 / 3$ $\square$
Part 1 of 3 $\arctan 29 \approx$ $\square$ $\square$ 。

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Problem 621

Question 9 (1 point) Saved $\cos \left(\frac{\pi}{2}-x\right)=\sin x$ True False
Question 10 (1 point) $\checkmark$ Saved $\cos (x+y)=\cos x+\cos y$ True False

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Problem 622

Determine the exact value of $\cot \frac{5 \pi}{3}$ .

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Problem 623

An equivalent trigonometric expression for $\cos \left[x+\frac{\pi}{2}\right)$ is $\sin x$ $-\sin x$ $\cos x$ none of the above
Question 15 (3 points) $\checkmark$ Saved
An equivalent trigonometric expression for $\tan (-x)$ is $\cot x$ $\tan x$ $-\cot x$ $-\tan x$

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Problem 624

ic equation for all values $-7 \leq x<7$ . $\sqrt{3} \cot \frac{1}{2} x=3$

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Problem 625

Find the amplitude and period for $-3 \cos (2 x)$ .

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Problem 626

Question Watch Vidè̀o
Solve the following equation for all values of $0 \leq \theta<2 \pi$ . $\tan ^{2} \theta-\tan \theta=0$

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Problem 627

$\frac{\csc \theta}{\sin \theta}$

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Problem 628

2. Find each ratio. $\operatorname{Sin} A=$ $\cos A=$ $\operatorname{Tan} A=$ $\operatorname{Sin} B=$ $\cos B=$ $\operatorname{Tan} B=$

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Problem 629

Simplify the expression $7 \cot^2 x - 7 \csc^2 x$ to a single trigonometric function with no denominator.

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Problem 630

```latex Un grupo de amigos ha viajado a México y visitan Chichén-Itzá. Una vez estando allá se acercan a admirar el Templo de Kukulkán que mide 30 m de altura y cuya base es un cuadrado de 55.3 m de lado. Para esto se ubican en línea recta de frente al templo como muestra la figura adjunta.
Claudia (punto C ) se encuentra en un punto tal que el ángulo de elevación desde el piso hasta la cima es de $26^{\circ}$ . Desde la posición de Felipe (Punto F) el ángulo de elevación desde el piso hasta la cima es de $37^{\circ}$ . La distancia desde la posición que toma Luis (punto L) hasta la cima del templo es de 103m.
¿Cuál es la medida del ángulo de elevación desde la posición de Luis hasta la cima del templo? El ángulo de elevación es de Respuesta grados sexagesimales Usa leyes de trigonometría ```

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Problem 631

a single trig function with no denominator. $\frac{-1-\tan ^{2} x}{\sec ^{2} x}$
Atrempl 1 out of:

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Problem 632

Watch Vidêo. he trigonometric equation for all values $0 \leq x<2 \pi$ . $\sqrt{3} \sec x=2$

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Problem 633

gonometric equation for all values $0 \leq x<2 \pi$ . $\csc x-2=0$

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Problem 634

Question Solve the trigonometric equation for all values $0 \leq x<\frac{14 \pi}{5}$ . $\sqrt{3} \cot \frac{5}{7} x=1$

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Problem 635

netric equation for all values $-3 \pi<x<3 \pi$ . $\cot \frac{1}{3} x-1=0$

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Problem 636

2 Rewrite $\cos 4 x$ in terms of $\cos x$ and powers of $\cos x$ . ( 3 points) (Note: The answer cannot have multiple angles of cosines)

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Problem 637

Solve for $x$ in the equation $2 \sin x = \sqrt{3} \tan x$ for $0^{\circ} \leq x \leq 360^{\circ}$ .

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Problem 638

Find $\theta$ such that $4 \sin^{2} \theta - 4 = -1$ for $0^{\circ} \leq \theta \leq 360^{\circ}$ .

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Problem 639

Solve for $0 \leq x \leq 360^{\circ}$ : $4 \cot ^{2} x - 9 \operatorname{cosec} x + 6 = 0$ .

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Problem 640

Prove that $\sin 60^{\circ} \cdot \tan 45^{\circ} \cdot \tan 30^{\circ} - \sin 240^{\circ} \cdot \tan 315^{\circ} \cdot \tan 210^{\circ} = 0$ .

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Problem 641

Prove the identity: $\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=\frac{2}{\sin x}$ .

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Problem 642

Find $x$ when $y=\frac{\pi}{4}$ and $y=\frac{3 \pi}{4}$ for $x=\csc(y)$ .

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Problem 643

Find the angle of depression from a camera 12 feet high to a point 5 feet high, 35 feet away from the wall.

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Problem 644

Find the height of a 63.9 m funicular track inclined at an angle of $40^{\circ} 2^{\prime}$ .

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Problem 645

Find the angle of elevation from a player's eyes at 6.2 ft to a rim at 10 ft, 15 ft away.

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Problem 646

Find the exact values of the six trigonometric functions for the angle $\theta$ with point $(-7,24)$ .

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Problem 647

Find the exact value of $\sec A$ if $\sin A = -\frac{5}{9}$ and $A$ is in quadrant 3.

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Problem 648

Calculate $\operatorname{tg} \frac{11 \pi}{6}$ .

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Problem 649

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{44}}{5}$ . Rationalize denominators if needed.

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Problem 650

Find the other trigonometric functions of $\theta$ if $\sin \theta=-\frac{\sqrt{3}}{6}$ and $\cos \theta>0$ .

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Problem 651

Find the remaining trigonometric functions of $\theta$ if $\sin \theta=\frac{\sqrt{3}}{6}$ and $\cos \theta>0$ . What is $\cos \theta$ ?

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Problem 652

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{20}}{4}$ . Simplify your answer, including any radicals.

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Problem 653

Determine the signs of the six trigonometric functions for the angle $261^{\circ}$ . Fill in the table.

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Problem 654

Find the quadrants for angle $\theta$ where $\cos \theta < 0$ and $\tan \theta > 0$ . Choose from: A. IV, B. II, C. I, D. III.

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Problem 655

Find the quadrant(s) where $\sin \alpha<0$ and $\sec \alpha<0$ . Answer as $1,2,3$ , or 4, separated by commas.

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Problem 656

Find the quadrant(s) for angles where $\csc \alpha > 0$ and $\cos \alpha > 0$ . Answer as $1,2,3$ , or 4.

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Problem 657

Find $\cos \theta$ if $\sin \theta=\frac{4}{5}$ and $\theta$ is in quadrant I.

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Problem 658

Find $\tan \theta$ if $\sin \theta = -\frac{1}{2}$ and $\theta$ is in quadrant IV.

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Problem 659

Find the remaining trigonometric functions of $\theta$ if $\tan \theta=-\frac{3}{4}$ in quadrant II.

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Problem 660

Find the exact values of $\sin \theta$ and $\cos \theta$ if $\tan \theta = -\frac{3}{4}$ in quadrant II.

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Problem 661

Find the other trigonometric functions of $\theta$ if $\tan \theta=-\frac{3}{4}$ in quadrant II.

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Problem 662

Find all trigonometric functions for $\theta$ if $\tan \theta=-\frac{3}{4}$ in quadrant II.

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Problem 663

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{117}}{6}$ . Simplify your answer.

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Problem 664

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{18}}{4}$ . Simplify and rationalize if needed.

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Problem 665

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{44}}{2}$ . Simplify your answer.

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Problem 666

Find (a) the complement and (b) the supplement of an angle measuring $17^{\circ} 15^{\prime}$ .

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Problem 667

Find $\csc \theta$ if $\cot \theta = -\frac{1}{6}$ and $\theta$ is in quadrant IV.

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Problem 668

A boat is 150 m from a lighthouse's base with a $34^{\circ}$ elevation angle. Find the boat's distance from the cliff.

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Problem 669

1. A boat sees a lighthouse foot at $34^{\circ}$ elevation; cliff height is 150 m. Find the boat's distance from the cliff base.
2. Flying at $037^{\circ}$ , turn left $45^{\circ}$ . What is the new heading?

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Problem 670

Find the equation of the function when $y=\sin \theta$ is stretched by $\frac{3}{2}$ , reflected in the $y$ axis, and shifted up 3 units.

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Problem 671

Find IJ.
Write your answer as an integer or as a decimal rounded to the nearest tenth. IJ = $\square$

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Problem 672

Find the amplitude and period for $-1 / 4 \sin (\pi x)$

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Problem 673

Find the reference angle for 192 degrees.

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Problem 674

1) $\cos \theta \times \tan \theta=\sin \theta$

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Problem 675

2 Using the triangle below, find the exact value of the given trig functions. $\sin \left(\frac{\theta}{2}\right)= \pm$ $\square$ $\cos \left(\frac{\theta}{2}\right)= \pm$ $\square$ $\tan \left(\frac{\theta}{2}\right)= \pm$ $\square$

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Problem 676

Question 4 (1 point) Determine the corresponding reciprocal ratio that corresponds to $\cos \theta=0.8$ . $\sec \theta=\frac{1}{2}$ $\sec \theta=\frac{5}{4}$ $\sec \theta=2$ $\sec \theta=\frac{4}{5}$

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Problem 677

Managed bookmarks Garage Open Back... Visit Website
Pre-Calculus A Unit Test Unit Test Active 1 4 5 6 7 8 9 10 $\square$ TIME REMAINING 03:31:58
Which shows all the exact solutions of $2 \sec ^{2} x-\tan ^{4} x=-1$ ? Give your answer in radians. $\frac{\pi}{3}+k \pi$ and $\frac{2 \pi}{3}+k \pi$ $\frac{\pi}{3}+2 k \pi$ and $\frac{5 \pi}{3}+2 k \pi$ $\frac{\pi}{4}+2 k \pi, \frac{3 \pi}{4}+2 k \pi, \frac{5 \pi}{4}+2 k \pi$ , and $\frac{7 \pi}{4}+2 k \pi$ $\frac{\pi}{3}+k \pi, \frac{2 \pi}{3}+k \pi, \frac{4 \pi}{3}+k \pi$ , and $\frac{5 \pi}{3}+k \pi$

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Problem 678

Unit Test Unit Test Active 1 3 4 5 6 7 8 9 10 TIME REMAINING 03:30:59
An object is attached to a spring that is stretched and released. The equation $d=-8 \cos \left(\frac{\pi}{6} t\right)$ models the distance, $d$ , of the object in inches above or below the rest position as a function of time, $t$ , in seconds. Approximately when will the object be 6 inches above the rest position? Round to the nearest hundredth, if necessary. 0 seconds 1.38 seconds 4.62 seconds 8 seconds

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Problem 679

Q. 4 Trigonometric ratios in similar right triangles $7 \times 7$
Find the sine of $\angle V$ . Submit

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Problem 680

1 3 4 5 5 1 8 (3) 10
Solve: $\cos (x+\pi)=\frac{1}{2}$ over the interval $\left[\frac{\pi}{2}, \pi\right]$ $\frac{\pi}{2}$ $\frac{2 \pi}{3}$ $\frac{3 \pi}{4}$ $\frac{5 \pi}{6}$

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Problem 681

1 $\square$ 3 4 5 6 1 13 y 10 $\square$
Let $\frac{\cos (2 x)}{\cos (x)+\sin (x)}=0$ where $0^{\circ} \leq x \leq 180^{\circ}$ . What are the possible values for $x$ ? $45^{\circ}$ only $135^{\circ}$ only $45^{\circ}$ or $225^{\circ}$ $135^{\circ}$ or $315^{\circ}$

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Problem 682

Unit Test Unit Test Active
1 3 4 5 6 7 8 9 10 $\square$
For $0^{\circ} \leq x<360^{\circ}$ , what are the solutions to $\cos \left(\frac{x}{2}\right)-\sin (x)=0$ ? $\left\{0^{\circ}, 60^{\circ}, 300^{\circ}\right\}$ $\left\{0^{\circ}, 120^{\circ}, 240^{\circ}\right\}$ $\left\{60^{\circ}, 180^{\circ}, 300^{\circ}\right\}$ $\left\{120^{\circ}, 180^{\circ}, 240^{\circ}\right\}$

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Problem 683

9) $\tan ^{4} k+\tan ^{2} k=\sec ^{4} k-\sec ^{2} k$

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Problem 684

Suppose that $\tan \alpha=\frac{3}{4}, \cos \alpha<0$ and $\cos \beta=\frac{1}{3}, \frac{3 \pi}{2}<\beta<2 \pi$ .
Find $\cos (2 \alpha)$

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Problem 685

What is the range of $y=\sec ^{-1}(x) ?$ $\left[-\frac{\pi}{2}, 0\right)$ and $\left(0, \frac{\pi}{2}\right]$ $\left[-\frac{\pi}{2}, 0\right]$ and $\left[0, \frac{\pi}{2}\right]$ $\left[0, \frac{\pi}{2}\right)$ and $\left(\frac{\pi}{2}, \pi\right]$ $\left[0, \frac{\pi}{2}\right]$ and $\left[\frac{\pi}{2}, \pi\right]$

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Problem 686

Given: $\cos \left(3 x-180^{\circ}\right)=-\frac{\sqrt{3}}{2}$ , where $0 \leq x<180^{\circ}$ Which values represent the solutions to the equation? $\left\{10^{\circ}, 110^{\circ}, 130^{\circ}\right\}$ $\left\{20^{\circ}, 100^{\circ}, 140^{\circ}\right\}$ $\left\{30^{\circ}, 330^{\circ}, 390^{\circ}\right\}$ $\left\{60^{\circ}, 300^{\circ}, 420^{\circ}\right\}$

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Problem 687

4. Determine the exact value of each trigonometric expression. a) $\sin 30^{\circ} \times \tan 60^{\circ}-\cos 30^{\circ}$ c) $\tan ^{2} 30^{\circ}-\cos ^{2} 45^{\circ}$ b) $2 \cos 45^{\circ} \times \sin 45^{\circ}$ d) $1-\frac{\sin 45^{\circ}}{\cos 45^{\circ}}$
5. Using exact values, show that $\sin ^{2} \theta+\cos ^{2} \theta=1$ for each angle. a) $\theta=30^{\circ}$ b) $\theta=45^{\circ}$ c) $\theta=60^{\circ}$
6. Using exact values, show that $\frac{\sin \theta}{\cos \theta}=\tan \theta$ for each angle. a) $\theta=30^{\circ}$ b) $\theta=45^{\circ}$ c) $\theta=60^{\circ}$

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Problem 688

Sketch the graph of the function. $f(x)=\arctan (4 x)$
Compare the graph to the graph of the parent inverse trigonometric function. The graph of $f(x)$ is $\arctan (x)$ with a ---Select--- $\square$ Read It

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Problem 689

4) Determine the values of $\sin 2 \theta, \cos 2 \theta$ , and $\tan 2 \theta$ , given $\cos \theta=\frac{3}{5}$ and $0 \leq \theta \leq \frac{\pi}{2}$

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Problem 690

Express each of the following as a single trigonometric ratio. a) $2 \sin 5 x \cos 5 x$ d) $\frac{2 \tan 4 x}{1-\tan ^{2} 4 x}$ b) $\cos ^{2} \theta-\sin ^{2} \theta$ e) $4 \sin ^{\prime} \theta \cos \theta$ c) $1-2 \sin ^{2} 3 x$ f) $2 \cos ^{2} \frac{\theta}{2}-1$

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Problem 691

The period, to the nearest tenth, of the function $y=\sin 0.25 x$ , where $x$ is in radians, is

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Problem 692

1. Determine the equation of the graph below in the form: a) $y=a \sin (x-c)$ if $a<0$ and there is a minimum possible horizontal phase shift. $\begin{array}{l} y=a \sin (x-c) \\ y=-4 \sin (x-\pi) \end{array}$ b) $y=a \cos (x-c)$ if $a>0$ and there is a minimum possible horizontal phase shift. $\begin{array}{l} y=a \cos (x-c) \\ y=4 \cos ( \end{array}$

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Problem 693

The cosine graph shown has a range $[-3,9]$ . The graph has an equation in the form $y=a \cos [b(x-c)]+d, a>0$ . Determine the equation if the graph has a minimum possible phase shift. max $=9$ min $=-5$ $\begin{array}{l} y=a \cos [b(x-c)]+d \\ a=\frac{\max -\min }{2} \quad d=\frac{m_{a x}+\min }{2} \\ a=\frac{4-(-3)}{2} \quad d=\frac{9+(-3)}{2} \\ a=6 \\ a=3 \end{array}$ $y=6 \cos [b(x-c)]+3$

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Problem 694

Question 13
Use Identities to find the exact value. $\cos \left(\frac{19 \pi}{12}\right)$ (A) $\frac{\sqrt{6}-\sqrt{2}}{4}$ (B) $\sqrt{2}-\sqrt{6}$ (C) $\frac{\sqrt{2}-\sqrt{6}}{4}$ (D) $-\sqrt{6}-\sqrt{2}$

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Problem 695

16) $\sec \cos ^{-1}-\sqrt{2}$

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Problem 696

$\cos ^{-1}(\sqrt{2} / 2)$

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Problem 697

Είναι μια κ μου Sin a + Cas also Sin'a + CosFa=k_1

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Problem 698

\text{هرگاه } x \text{ باشد، بیشترین مقدار } \tan x + \cot x \text{ کدام است؟}

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Problem 699

Ground Level [Ground level will be from the point where the canon was shot out from $\Delta y=0$ ]. 1) Set the cannon to have an initial speed of $20 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will go father: if it is set at a 25-degree angle, or if it is set at a 35-degree angle? (1 pt) Hypothesis: Concluslons: 2) Set the cannon to have an initial speed of $20 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will go father: if it Is set at a 60-degree angle, or if it is set at a 70-degree angle? (1 pt) Hypothesis: Conclusions: 3) Set the cannon to have an initial speed of $15 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will go the highest: If it is set at a 25-degree angle, or if it is set at a 35-degree angle? (1 pt) Hypothesis: Concluslons: 4) Set the cannon to have an initial speed of $15 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will go highest: If It is set at a 60-degree angle, or if it is set at a 70 -degree angle? (1 pt) Hypothesis: Conclusions: 5) Set the cannon to have an initial speed of $25 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will be in the alr for the longest time: if it is set at a 25-degree angle, or If it is set at a 35-degree angle? (1 pt) Hypothes/s: Conclusions: 6) Set the cannon to have an initial speed of $15 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will be in the air for the longest time: if it is set at a 60-degree angle, or If it is set at a 70 -degree angle? (1 pt) Hypothesis: Conclusions:

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Problem 700

Besar sudut $30^{\circ} 12$ - dalam satuan radian adalah (A) $\frac{151}{900} \pi \mathrm{rad}$ . (B) $\frac{152}{900} \pi \mathrm{rad}$ . (C) $\frac{153}{900} \pi \mathrm{rad}$ . (D) $\frac{154}{900} \pi \mathrm{rad}$ . (E) $\frac{155}{900} \pi \mathrm{rad}$ .

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1 ...4 5 6 7 8 9 10 ...23

Trigonometry

Problem 601

10. Find the exact value of cos⁡I\cos IcosI in simplest radical form.

Problem 602

Find the exact value of tan⁡O\tan OtanO in simplest radical form.

Problem 603

Problem 604

Problem 605

Rewrite each expression as a single trigonometric ratio, and then evaluate the ratio. a) tan⁡170∘−tan⁡110∘1+tan⁡170∘tan⁡110∘\frac{\tan 170^{\circ}-\tan 110^{\circ}}{1+\tan 170^{\circ} \tan 110^{\circ}}1+tan170∘tan110∘tan170∘−tan110∘​

Problem 606

Problem 607

Problem 608

Problem 609

Problem 610

Problem 611

Problem 612

Part 1 of 3Write the ratios for sin⁡M,cos⁡M\sin M, \cos MsinM,cosM, and tan⁡M\tan MtanM.

Problem 613

19-34 - Amplitude and Period of the function, and sketch its grap19. y=cos⁡2xy=\cos 2 xy=cos2x

Problem 614

Find the measure of side c .

Problem 615

Find the value of xxx.

Problem 616

Problem 617

tower?61. Elevation of a Kite A tourist is lying on the beach, flying a kite. The tourist holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be 50∘50^{\circ}50∘. If the string is 450 ft long, how high is the kite above the ground?

Problem 618

Use a calculator to approximate the function values in both radians and degrees to 4 decimal places.Part: 0/30 / 30/3Part 1 of 3 arctan⁡29≈□rad≈□∘\arctan 29 \approx \square \mathrm{rad} \approx \square^{\circ}arctan29≈□rad≈□∘

Problem 619

33-40 ■ Value of an Expression expression.33. cos⁡(sin⁡−1(45))\cos \left(\sin ^{-1}\left(\frac{4}{5}\right)\right)cos(sin−1(54​))

Problem 620

Use a calculator to approximate the function values in both radians and degrees to 4 decimal places.Part: 0/30 / 30/3 □\square□Part 1 of 3 arctan⁡29≈\arctan 29 \approxarctan29≈ □\square□ □\square□。

Problem 621

Question 9 (1 point) Saved cos⁡(π2−x)=sin⁡x\cos \left(\frac{\pi}{2}-x\right)=\sin xcos(2π​−x)=sinx True FalseQuestion 10 (1 point) ✓\checkmark✓ Saved cos⁡(x+y)=cos⁡x+cos⁡y\cos (x+y)=\cos x+\cos ycos(x+y)=cosx+cosy True False

Problem 622

Determine the exact value of cot⁡5π3\cot \frac{5 \pi}{3}cot35π​.

Problem 623

Problem 624

ic equation for all values −7≤x<7-7 \leq x<7−7≤x<7. 3cot⁡12x=3\sqrt{3} \cot \frac{1}{2} x=33​cot21​x=3

Problem 625

Find the amplitude and period for −3cos⁡(2x)-3 \cos (2 x)−3cos(2x).

Problem 626

Question Watch Vidè̀oSolve the following equation for all values of 0≤θ<2π0 \leq \theta<2 \pi0≤θ<2π. tan⁡2θ−tan⁡θ=0\tan ^{2} \theta-\tan \theta=0tan2θ−tanθ=0

Problem 627

csc⁡θsin⁡θ\frac{\csc \theta}{\sin \theta}sinθcscθ​

Problem 628

2. Find each ratio. Sin⁡A=\operatorname{Sin} A=SinA= cos⁡A=\cos A=cosA= Tan⁡A=\operatorname{Tan} A=TanA= Sin⁡B=\operatorname{Sin} B=SinB= cos⁡B=\cos B=cosB= Tan⁡B=\operatorname{Tan} B=TanB=

Problem 629

Simplify the expression 7cot⁡2x−7csc⁡2x7 \cot^2 x - 7 \csc^2 x7cot2x−7csc2x to a single trigonometric function with no denominator.

Problem 630

Problem 631

a single trig function with no denominator. −1−tan⁡2xsec⁡2x\frac{-1-\tan ^{2} x}{\sec ^{2} x}sec2x−1−tan2x​Atrempl 1 out of:

Problem 632

Watch Vidêo. he trigonometric equation for all values 0≤x<2π0 \leq x<2 \pi0≤x<2π. 3sec⁡x=2\sqrt{3} \sec x=23​secx=2

Problem 633

gonometric equation for all values 0≤x<2π0 \leq x<2 \pi0≤x<2π. csc⁡x−2=0\csc x-2=0cscx−2=0

Problem 634

Question Solve the trigonometric equation for all values 0≤x<14π50 \leq x<\frac{14 \pi}{5}0≤x<514π​. 3cot⁡57x=1\sqrt{3} \cot \frac{5}{7} x=13​cot75​x=1

Problem 635

netric equation for all values −3π<x<3π-3 \pi<x<3 \pi−3π<x<3π. cot⁡13x−1=0\cot \frac{1}{3} x-1=0cot31​x−1=0

Problem 636

2 Rewrite cos⁡4x\cos 4 xcos4x in terms of cos⁡x\cos xcosx and powers of cos⁡x\cos xcosx. ( 3 points) (Note: The answer cannot have multiple angles of cosines)

Problem 637

Solve for xxx in the equation 2sin⁡x=3tan⁡x2 \sin x = \sqrt{3} \tan x2sinx=3​tanx for 0∘≤x≤360∘0^{\circ} \leq x \leq 360^{\circ}0∘≤x≤360∘.

Problem 638

Find θ\thetaθ such that 4sin⁡2θ−4=−14 \sin^{2} \theta - 4 = -14sin2θ−4=−1 for 0∘≤θ≤360∘0^{\circ} \leq \theta \leq 360^{\circ}0∘≤θ≤360∘.

Problem 639

Solve for 0≤x≤360∘0 \leq x \leq 360^{\circ}0≤x≤360∘: 4cot⁡2x−9cosec⁡x+6=04 \cot ^{2} x - 9 \operatorname{cosec} x + 6 = 04cot2x−9cosecx+6=0.

Problem 640

Prove that sin⁡60∘⋅tan⁡45∘⋅tan⁡30∘−sin⁡240∘⋅tan⁡315∘⋅tan⁡210∘=0\sin 60^{\circ} \cdot \tan 45^{\circ} \cdot \tan 30^{\circ} - \sin 240^{\circ} \cdot \tan 315^{\circ} \cdot \tan 210^{\circ} = 0sin60∘⋅tan45∘⋅tan30∘−sin240∘⋅tan315∘⋅tan210∘=0.

Problem 641

Prove the identity: sin⁡x1+cos⁡x+1+cos⁡xsin⁡x=2sin⁡x\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=\frac{2}{\sin x}1+cosxsinx​+sinx1+cosx​=sinx2​.

Problem 642

Find xxx when y=π4y=\frac{\pi}{4}y=4π​ and y=3π4y=\frac{3 \pi}{4}y=43π​ for x=csc⁡(y)x=\csc(y)x=csc(y).

Problem 643

Find the angle of depression from a camera 12 feet high to a point 5 feet high, 35 feet away from the wall.

Problem 644

Find the height of a 63.9 m funicular track inclined at an angle of 40∘2′40^{\circ} 2^{\prime}40∘2′.

Problem 645

Find the angle of elevation from a player's eyes at 6.2 ft to a rim at 10 ft, 15 ft away.

10. Find the exact value of $\cos I$ in simplest radical form.

Find the exact value of $\tan O$ in simplest radical form.

Rewrite each expression as a single trigonometric ratio, and then evaluate the ratio. a) $\frac{\tan 170^{\circ}-\tan 110^{\circ}}{1+\tan 170^{\circ} \tan 110^{\circ}}$

Part 1 of 3
Write the ratios for $\sin M, \cos M$ , and $\tan M$ .

19-34 - Amplitude and Period of the function, and sketch its grap
19. $y=\cos 2 x$

Find the value of $x$ .

tower?
61. Elevation of a Kite A tourist is lying on the beach, flying a kite. The tourist holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be $50^{\circ}$ . If the string is 450 ft long, how high is the kite above the ground?

Use a calculator to approximate the function values in both radians and degrees to 4 decimal places.
Part: $0 / 3$
Part 1 of 3 $\arctan 29 \approx \square \mathrm{rad} \approx \square^{\circ}$

33-40 ■ Value of an Expression expression.
33. $\cos \left(\sin ^{-1}\left(\frac{4}{5}\right)\right)$

Use a calculator to approximate the function values in both radians and degrees to 4 decimal places.
Part: $0 / 3$ $\square$
Part 1 of 3 $\arctan 29 \approx$ $\square$ $\square$ 。

Question 9 (1 point) Saved $\cos \left(\frac{\pi}{2}-x\right)=\sin x$ True False
Question 10 (1 point) $\checkmark$ Saved $\cos (x+y)=\cos x+\cos y$ True False

Determine the exact value of $\cot \frac{5 \pi}{3}$ .

ic equation for all values $-7 \leq x<7$ . $\sqrt{3} \cot \frac{1}{2} x=3$

Find the amplitude and period for $-3 \cos (2 x)$ .

Question Watch Vidè̀o
Solve the following equation for all values of $0 \leq \theta<2 \pi$ . $\tan ^{2} \theta-\tan \theta=0$

$\frac{\csc \theta}{\sin \theta}$

2. Find each ratio. $\operatorname{Sin} A=$ $\cos A=$ $\operatorname{Tan} A=$ $\operatorname{Sin} B=$ $\cos B=$ $\operatorname{Tan} B=$

Simplify the expression $7 \cot^2 x - 7 \csc^2 x$ to a single trigonometric function with no denominator.

a single trig function with no denominator. $\frac{-1-\tan ^{2} x}{\sec ^{2} x}$
Atrempl 1 out of:

Watch Vidêo. he trigonometric equation for all values $0 \leq x<2 \pi$ . $\sqrt{3} \sec x=2$

gonometric equation for all values $0 \leq x<2 \pi$ . $\csc x-2=0$

Question Solve the trigonometric equation for all values $0 \leq x<\frac{14 \pi}{5}$ . $\sqrt{3} \cot \frac{5}{7} x=1$

netric equation for all values $-3 \pi<x<3 \pi$ . $\cot \frac{1}{3} x-1=0$

2 Rewrite $\cos 4 x$ in terms of $\cos x$ and powers of $\cos x$ . ( 3 points) (Note: The answer cannot have multiple angles of cosines)

Solve for $x$ in the equation $2 \sin x = \sqrt{3} \tan x$ for $0^{\circ} \leq x \leq 360^{\circ}$ .

Find $\theta$ such that $4 \sin^{2} \theta - 4 = -1$ for $0^{\circ} \leq \theta \leq 360^{\circ}$ .

Solve for $0 \leq x \leq 360^{\circ}$ : $4 \cot ^{2} x - 9 \operatorname{cosec} x + 6 = 0$ .

Prove that $\sin 60^{\circ} \cdot \tan 45^{\circ} \cdot \tan 30^{\circ} - \sin 240^{\circ} \cdot \tan 315^{\circ} \cdot \tan 210^{\circ} = 0$ .

Prove the identity: $\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=\frac{2}{\sin x}$ .

Find $x$ when $y=\frac{\pi}{4}$ and $y=\frac{3 \pi}{4}$ for $x=\csc(y)$ .

Find the height of a 63.9 m funicular track inclined at an angle of $40^{\circ} 2^{\prime}$ .

Find the exact values of the six trigonometric functions for the angle $\theta$ with point $(-7,24)$ .

Find the exact value of $\sec A$ if $\sin A = -\frac{5}{9}$ and $A$ is in quadrant 3.

Calculate $\operatorname{tg} \frac{11 \pi}{6}$ .

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{44}}{5}$ . Rationalize denominators if needed.

Find the other trigonometric functions of $\theta$ if $\sin \theta=-\frac{\sqrt{3}}{6}$ and $\cos \theta>0$ .

Find the remaining trigonometric functions of $\theta$ if $\sin \theta=\frac{\sqrt{3}}{6}$ and $\cos \theta>0$ . What is $\cos \theta$ ?

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{20}}{4}$ . Simplify your answer, including any radicals.

Determine the signs of the six trigonometric functions for the angle $261^{\circ}$ . Fill in the table.

Find the quadrants for angle $\theta$ where $\cos \theta < 0$ and $\tan \theta > 0$ . Choose from: A. IV, B. II, C. I, D. III.

Find the quadrant(s) where $\sin \alpha<0$ and $\sec \alpha<0$ . Answer as $1,2,3$ , or 4, separated by commas.

Find the quadrant(s) for angles where $\csc \alpha > 0$ and $\cos \alpha > 0$ . Answer as $1,2,3$ , or 4.

Find $\cos \theta$ if $\sin \theta=\frac{4}{5}$ and $\theta$ is in quadrant I.

Find $\tan \theta$ if $\sin \theta = -\frac{1}{2}$ and $\theta$ is in quadrant IV.

Find the remaining trigonometric functions of $\theta$ if $\tan \theta=-\frac{3}{4}$ in quadrant II.

Find the exact values of $\sin \theta$ and $\cos \theta$ if $\tan \theta = -\frac{3}{4}$ in quadrant II.

Find the other trigonometric functions of $\theta$ if $\tan \theta=-\frac{3}{4}$ in quadrant II.

Find all trigonometric functions for $\theta$ if $\tan \theta=-\frac{3}{4}$ in quadrant II.

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{117}}{6}$ . Simplify your answer.

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{18}}{4}$ . Simplify and rationalize if needed.

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{44}}{2}$ . Simplify your answer.

Find (a) the complement and (b) the supplement of an angle measuring $17^{\circ} 15^{\prime}$ .

Find $\csc \theta$ if $\cot \theta = -\frac{1}{6}$ and $\theta$ is in quadrant IV.

A boat is 150 m from a lighthouse's base with a $34^{\circ}$ elevation angle. Find the boat's distance from the cliff.

1. A boat sees a lighthouse foot at $34^{\circ}$ elevation; cliff height is 150 m. Find the boat's distance from the cliff base.
2. Flying at $037^{\circ}$ , turn left $45^{\circ}$ . What is the new heading?

Find the equation of the function when $y=\sin \theta$ is stretched by $\frac{3}{2}$ , reflected in the $y$ axis, and shifted up 3 units.

Find IJ.
Write your answer as an integer or as a decimal rounded to the nearest tenth. IJ = $\square$

Find the amplitude and period for $-1 / 4 \sin (\pi x)$

1) $\cos \theta \times \tan \theta=\sin \theta$