Trigonometry

Problem 701

If $\cos ^{2} x \sin ^{4} x=A+B \cos 2 x+C \cos 4 x+D \cos 2 x \cos 4 x$ then $A=$ $B=$ $C=$ $D=$

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Problem 702

Find the reference angle for $24^{\circ}$ .

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Problem 703

A
9. Determine the amplitude of the following function. $y=0.5 \sin (x-2)$ A. 0.5 B. 1 C. 2 D. 0
10. Determine the period of the following function. $y=0.5 \sin (x-2)$ A. $180^{\circ}$ B. $360^{\circ}$ C. $720^{\circ}$ D. $1080^{\circ}$
11. Determine the midline of the following function. $y=\cos \frac{1}{3} x+12$ A. $y=12$ B. $y=3$ C. $y=4$ D. $y=0$
12. Determine the midline of the following function. $y=0.5 \sin (x-2)$ A. $y=-2$ B. $y=0.5$ C. $y=0$ D. $y=2$
13. Determine the range of the following function. $\begin{array}{l} y=3 \sin 2\left(x+90^{\circ}\right)-1 \end{array}$ A. $\{y \mid-3 \leq y \leq 3, y \in \mathrm{R}\}$ B. $\{y \mid-2 \leq y \leq 4, y \in R\}$ C. $\{y \mid-4 \leq y \leq 2, y \in R\}$ D. $\{y \mid y \in R\}$ B. 2.6 C. 4.7 D. 5.4

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Problem 704

1. Find the exact value of the expression $\cos (\pi) \cdot \cos \left(\frac{3 \pi}{4}\right)+\sin (\pi) \cdot \sin \left(\frac{3 \pi}{4}\right)$ .

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Problem 705

2. The graph of a sinusoidal function has a maximum at $(4,3)$ followed by a minimum at $(8,1)$ . a) Describe the graph of the function by stating the amplitude, equation of its midline, range, and period. Show your work. ( 2 points -0.5 point for each description) b) Determine the $y$ -value of the function when $x=10$ . Show your work. 2 points

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Problem 706

$\sin ^{-1}\left(-\frac{1}{2}\right)$

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Problem 707

$\cos ^{-1}\left(-\frac{\sqrt{2}}{2}\right)$

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Problem 708

$\arccos \frac{1}{2}$

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Problem 709

$\tan ^{-1}(-1)$

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Problem 710

Find the exact values of $r$ and $y$ given $B=76^{\circ}$ , and $x=6$ . NOTE: You will need to use trigonometric functions in your answers. $r=$ $\square$ $B=76^{\circ}$ $y=$

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Problem 711

One of the sides $x, y$ and $r$ of the triangle in the figure below is given. Find exact values of the other two sides.
Find the values of $r$ and $y$ in the figure, given that $B=12^{\circ}, x=\lambda$ . $r=\lambda / \cos 12^{\circ}$ and $y=\lambda / \tan 12^{\circ}$ $r=\lambda / \sin 12^{\circ}$ and $y=\lambda / \cos 12^{\circ}$ $r=\lambda / \cos 12^{\circ}$ and $y=\lambda / \cos 12^{\circ}$ $r=\lambda / \sin 12^{\circ}$ and $y=\lambda / \tan 12^{\circ}$

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Problem 712

$2 \cos x+1=0,-\pi \leq x \leq 2 \pi$

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Problem 713

The graph to the right is a function of the form $y=A \cos (B x-C)+D, B>0$ . The five quarter points of one cycle of the graph, from left to right, are given below. These five quarter points on the graph correspond to the five quarter points on the graph of $y=\cos x$ over the interval $[0,2 \pi]$ . Determine the equation of the specific function that is represented by the given graph based on the association of the labeled quarter points and the quarter points of the graph of $y=\cos x$ over the interval $[0,2 \pi]$ .
The quarter points are $\left(\frac{\pi}{10}, 5\right),\left(\frac{\pi}{5}, 2\right),\left(\frac{3 \pi}{10},-1\right),\left(\frac{2 \pi}{5}, 2\right)$ , and $\left(\frac{\pi}{2}, 5\right)$ .
What is the function of the form $y=A \cos (B x-C)+D$ , where $B>0$ and $-\pi<C<\pi$ , that is represented by the given graph? $\square$ (Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the equation.)

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Problem 714

5. Prove the following identities a) $\cos (\beta)+\tan (\beta) \sin (\beta)=\sec (\beta)$

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Problem 715

Current Attempt in Progress (a) Find an angle $\theta$ , with $0^{\circ}<\theta<360^{\circ}$ , that has the same cosine as $50^{\circ}$ (but is not $50^{\circ}$ ). $\theta=$ $\square$ - (b) Find an angle $\theta$ , with $0^{\circ}<\theta<360^{\circ}$ , that has the same sine as $50^{\circ}$ (but is not $50^{\circ}$ ). $\theta=\boxed{\mathbf{i}}$

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Problem 716

5) $\frac{\cos \theta}{\sec \theta}-\frac{\sin \theta}{\cot \theta}=\frac{\cos \theta \cot \theta-\tan \theta}{\csc \theta}$

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Problem 717

$\csc ^{2}(x)-\csc (x) \cot (x)=\frac{1}{1+\cos (x)}$

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Problem 718

18. The graph of $y=2 \sin b(x-c)+1$ is shown below. Determine a value of $c$ . A. $\frac{2 \pi}{7}$ C. 2 B. $\frac{\pi}{4}$ D. $\frac{2 \pi}{2}$

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Problem 719

Find the amplitude of the sinusoidal function.
Simplify any fractions. amplitude $=$ $\square$

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Problem 720

$\frac{\sin (\theta)+1}{1-\sin (\theta)}=(\tan (\theta)+\sec (\theta))^{2}$

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Problem 721

Part 1 of 3
Determine the number of cycles the following sine function has in the interval from 0 to $2 \pi$ . Find the amplitude and period of the function $y=-4 \sin 2 \pi \theta$
The given sine function has $\square$ cycle(s). (Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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Problem 722

A particle in the ocean moves with a wave. The motion of the particle can be modeled by the cosine function. If a 10 in. wave occurs every 6 s , write a function that models the height of the particle in inches $y$ as it moves in seconds $x$ . What is the period of the function?
A function that models the height of the particle is $\square$ (Simplify your answer. Type an equation. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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Problem 723

One cycle of the graph of a trigonometric function of the form $y=A \boldsymbol{\operatorname { s i n }}(B x)$ or $y=A \boldsymbol{\operatorname { c o s }}(B x)$ is given. Determine the equation of the function represented by the following graph.
What function of the form $y=A \sin (B x)$ or $y=A \cos (B x), B>0$ is represented by the given graph? $\square$ (bse integers or fractions for any numbers in the equation.)

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Problem 724

MCR3U1 Unit 5 - Trigonometry Name: $\qquad$ $\operatorname{Can} 31$ Date: $\qquad$
3. Determine the exact value of $\sin 225^{\circ}$ . Include a diagram. $270-225=50^{\circ}$
4. Determine the value(s) of $\theta$ where $\csc \theta=-2$ for $\theta$ between $0^{\circ}$ and $360^{\circ}$ . Include a diagram.

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Problem 725

One cycle of the graph of a trigonometric function of the form $y=A \sin (B x)$ or $y=A \cos (B x)$ is given. Determine the equation of the function represented by the following graph
What function of the form $y=A \sin (B x)$ or $y=A \cos (B x), B>0$ is represented by the given graph? $\square$ (Use integers or fractions lor any numbers in the equation)

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Problem 726

Find the cosine of $\angle G$ .
Write your answer in simplified, rationalized form. Do not round. $\cos (G)=$

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Problem 727

The accompanying graph shows a sinusoidal function. Complete parts a) through c) below. a) What is the period of this function?
The period is $\square$

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Problem 728

Prove this Idenity is true $\frac{1+\cos 2 x}{\sin 2 x}=\cot x$

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Problem 729

1. Conaider two angles, $\mu$ and $\varphi$ such that $\begin{array}{l} \text { maider two angles, } \mu \text { and } \varphi \text { such that } \\ \frac{\pi}{2} \leq \mu \leq \frac{\pi}{2} \text { and } \sin \mu=\frac{2}{5} \quad \frac{2}{2} \leq \varphi \leq \frac{1 \pi}{2} \text { and } \sin \varphi=-\frac{12}{13} \end{array}$ a. Skitch $\mu$ and $\varphi$ on separate Cartesian planes. b. Determine the eact value of $\cos (\mu+\varphi)$ .

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Problem 730

Question 9 10 pts
Find the exact value of $2 \cos \left(15^{\circ}\right) \sin \left(15^{\circ}\right)$ $\frac{1}{2}$ 1 30 $\frac{\sqrt{3}}{2}$

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Problem 731

Consider the following. $t=\frac{5 \pi}{3}$ (a) Find the reference number $\bar{t}$ for the value of $t$ . $\bar{t}=\frac{\pi}{3}$ (b) Find the terminal point determined by $t$ . $(x, y)=(\square)$ Need Help? Read It

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Problem 732

$B=75^{\circ}, c=4, a=3$ w window) 3 Points $\begin{array}{l} b=\square \\ C=\square \\ A=\square \end{array}$

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Problem 733

Score: 6/10
Find the exact value of $\sin 135^{\circ}$
Answer

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Problem 734

Use a calculator to evaluate arcsin( 0.55 ) to 4 decimal places in radian

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Problem 735

Use a calculator to evaluate $\tan ^{-1}(51)$ to 2 decimal places in degrees. If necessary, use 3.1416 as an approximation to pi.

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Problem 736

Simplify the expression $\cot \left(\sin ^{-1}\left(\frac{x}{2}\right)\right)$ . Choose one correct answer from given answers. $\frac{-\sqrt{x^{2}+4}}{x}$ $\frac{\sqrt{x^{2}-4}}{x}$ $\frac{\sqrt{x^{2}+4}}{2 x}$ $\frac{\sqrt{-x^{2}+4}}{x}$

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Problem 737

$\cos \left(x+\frac{\pi}{6}\right)=\frac{\sqrt{2}}{2}$ a. Set for general solution
6. Set on the interval $[0,2 \pi)$

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Problem 738

Find measures of a positive angle and a negative angle coterminal with $-\frac{29 \pi}{5}$ radians and distinct from it.
Give the answers in simplest form. positive angle = $\square$ radians negative angle $=$ $\square$ radians

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Problem 739

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Current Attempt in Progress
Your answer is incorrect.
In which quadrant is a point with the polar coordinate $\theta=2.1 \pi$ ?
Quadrant II eTextbook and Media
Hint
Save for Later Attempts: 1 of 3 used Submit Answer

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Problem 740

What is the correct equation for the following function? $y=\cos 2 x$ $y=\frac{1}{2} \cos x$ $y=2 \cos x$ $y=\cos \frac{1}{2} x$

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Problem 741

Suppose that $\alpha$ and $\beta$ are angles in quadrant I with $\sin \alpha=\frac{8}{17}$ and $\cos \beta=\frac{20}{29}$ . Compute the exact value of $\sin (\alpha+\beta)$ . $\sin (\alpha+\beta)=$ $\square$

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Problem 742

Use the sum or difference formula for cosine to find the exact value for $\cos \left(105^{\circ}\right)$ $\cos \left(105^{\circ}\right)=$

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Problem 743

Use a compound angle formula to determine the exact value of $\tan \frac{\pi}{12}$

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Problem 744

Using the Law of Sines to solve the all possible triangles if $\angle A=119^{\circ}, a=30, b=19$ . If no answer exists, enter DNE for all answers. $\angle B$ is $\square$ degrees; $\angle C$ is $\square$ degrees; $c=\square ;$

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Problem 745

1) Calcular el valor numérico de la siguiente expresión: $\frac{\operatorname{Cos}^{2}\left(30^{\circ}\right)+\operatorname{Sen} 1845^{\circ}-\operatorname{tg}^{2}\left(300^{\circ}\right) \cdot \operatorname{Cos}^{2}\left(240^{\circ}\right)+\operatorname{Sen} 45^{\circ} \cdot \operatorname{Cos} 180^{\circ}}{\operatorname{tg} 45^{\circ} \cdot \operatorname{ctg} 45^{\circ}}$

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Problem 746

Use half angle formula $(\sin (2 x))^{4}=$

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Problem 747

Find two positive and two negative angles coterminal with $A = -630^{\circ}$ .

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Problem 748

Convert the angle $-51^{\circ} 30^{\prime}$ to decimal degree notation.

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Problem 749

Convert the angle $-75^{\circ} 3^{\prime}$ to decimal degrees.

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Problem 750

Convert the angle $-41^{\circ} 54^{\prime}$ to decimal degrees.

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Problem 751

Is it true that the tangent of an angle in a right triangle equals the opposite side divided by the hypotenuse? A. Yes B. No C. Maybe D. Sometimes E. Not applicable

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Problem 752

In a right triangle, the cosine ratio is equal to the side adjacent to the angle divided by the hypotenuse.

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Problem 753

Calculate $\cos 48^{\circ}$ and round to two decimal places. Options: A. 0.50 B. 1 C. 0.67 D. 0.48 E. None.

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Problem 754

A train track rises at $10^{\circ}$ . How high does it rise over 230 feet? Estimate to two decimal places. A. 121.34 in B. 45.85 ft C. 40.56 ft D. 115.36 in E. None.

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Problem 755

Find the legs of a right triangle with an angle of $65^{\circ}$ and a hypotenuse of 12. Round to two decimals.

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Problem 756

Simplify $\tan 100^{\circ} + 4 \sin 100^{\circ}$ .

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Problem 757

Match each trigonometric function with its value:
sin 60° = ?, cos 45° = ?, tan 45° = ?, sec 30° = ?, csc 30° = ?, cot 60° = ?
Choices: $\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}, \frac{2 \sqrt{3}}{3}, 1, \frac{\sqrt{3}}{2}, \frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{2}$

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Problem 758

Find $\tan B$ given $a=5$ , $b=12$ , and $c=13$ . Also, $\sin B=\frac{12}{13}$ , $\cos B=\frac{5}{13}$ .

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Problem 759

Find side $c$ with $a=5$ , $b=12$ . Then calculate $\sin B$ and simplify the results.

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Problem 760

Given sides $a=5$ and $b=12$ , find $c$ , $\sin B$ , $\cos B$ , $\tan B$ , and $\sec B$ .

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Problem 761

Find the trigonometric functions for angle B given $a=5$ , $b=12$ , $c=13$ : $\sin B$ , $\cos B$ , $\tan B$ , $\sec B$ , $\csc B$ .

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Problem 762

Find the value of $\csc 45^{\circ}$ . Simplify your answer with integers or fractions.

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Problem 763

Rewrite $\sin 61^{\circ}$ using its cofunction. What is $\sin 61^{\circ}=$ ? (Provide the answer without the degree symbol.)

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Problem 764

Rewrite $\tan 38^{\circ}$ using its cofunction. What is the simplified answer?

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Problem 765

Calculate the exact value of $\sec 30^{\circ}$ . Simplify your answer with integers or fractions.

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Problem 766

Find the exact value of $\sin 60^{\circ}$ . Simplify your answer with radicals, integers, or fractions.

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Problem 767

Find the exact value of $\tan 30^{\circ}$ . Simplify your answer with integers or fractions.

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Problem 768

Rewrite $\tan 74^{\circ}$ using its cofunction. What is $\tan 74^{\circ}=$ ? Simplify your answer without the degree symbol.

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Problem 769

Calculate the exact value of $\csc 45^{\circ}$ . Simplify your answer using integers or fractions.

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Problem 770

Find the smallest positive angle (in degrees) coterminal with $A=247^{\circ}$ .

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Problem 771

Find $\theta$ using the equation $\cos \theta=\frac{5}{12}$ . Round to the nearest degree if necessary.

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Problem 772

A building casts a 130 ft shadow with the Sun at an $82.9^{\circ}$ angle. Find the building's height.

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Problem 773

Kristen's telescope is 5 ft high. At an $8^{\circ}$ angle, how tall is the tree 120 ft away?

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Problem 774

Find the angle of elevation for a jet that travels 56 miles horizontally and reaches an altitude of 12.6 miles.

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Problem 775

Find the angle of elevation of the sun when a 40 ft tree casts a 58 ft shadow.

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Problem 776

Find the height of a balloon on a 40-foot string at a $50^{\circ}$ angle with the ground.

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Problem 777

Find 3 angles coterminal with $77^{\circ}$ , including at least one negative and one positive angle.

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Problem 778

Find 3 angles coterminal with $39^{\circ}$ , including at least one negative and one positive angle.

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Problem 779

Find 3 angles coterminal with $201^{\circ}$ , including at least one negative and one positive angle.

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Problem 780

Find 3 angles coterminal with $201^{\circ}$ , including at least one negative and one positive angle.

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Problem 781

Draw the angle $-240^{\circ}$ in standard position and identify its quadrant.

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Problem 782

Solve the equations: a) $\frac{2}{\sin x}-\frac{\sin x}{1+\cos x}=\frac{1+\cos x}{\sin x}$ ; c) $\operatorname{tg} x\left(\operatorname{cotg}^{2} x-1\right)=\operatorname{cotg} x\left(1-\operatorname{tg}^{2} x\right)$ .

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Problem 783

Find the distance from the base of the left field wall to the point below the seats, given height 90 ft and angle $14^{\circ}$ .

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Problem 784

A wire stretches from a pole's top to a point 18 ft from its base at a $52^{\circ}$ angle. Find the pole's height and wire length.

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Problem 785

Find the height of a smokestack that casts a shadow of $1580$ ft when the Sun's angle of elevation is $38^{\circ}$ .

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Problem 786

Find the angle of inclination of a $450-\mathrm{ft}$ ramp that rises $31-\mathrm{ft}$ to the nearest tenth of a degree.

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Problem 787

Sam sees Long's Peak at $31^{\circ}$ from a distance. After moving 1000 ft closer, the angle is $37^{\circ}$ . Find the height difference.

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Problem 788

Convert the angle $-76^{\circ} 12^{\prime}$ to decimal degree notation.

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Problem 789

Calculate the value of $\cos 45^{\circ}$ . Simplify your answer with radicals, integers, or fractions.

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Problem 790

Find the exact value of $\tan 45^{\circ}$ . What is $\tan 45^{\circ}=$ ? Simplify your answer.

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Problem 791

Use an addition or subtraction formula to write the expression as a trigonometric function of one number: $\cos \frac{3 \pi}{7} \cos \frac{2 \pi}{21}+\sin \frac{3 \pi}{7} \sin \frac{2 \pi}{21}=\cos \frac{\pi}{A}=\frac{B}{2}$ . $B=$

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Problem 792

Use an addition or subtraction formula to write the expression as a trigonometric functi $\frac{\tan 73^{\circ}-\tan 13^{\circ}}{1+\tan 73^{\circ} \tan 13^{\circ}}=\tan A^{\circ}=\sqrt{B}$ A = $B=$ Submit Question

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Problem 793

Question Watch Video Show Examples
In $\triangle B C D$ , the measure of $\angle D=90^{\circ}, C B=85, B D=36$ , and $D C=77$ . What is the value of the cosine of $\angle \mathrm{B}$ to the nearest hundredth?
Answer Attempt 1 out of 2 Submit Answer Sign out Nov 22 7:48

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Problem 794

Find an angle $\phi$ , with $0^{\circ}<\phi<360^{\circ}$ that has the same a) cosine as $52^{\circ}$ i 308 degrees b) sine as $52^{\circ}$ $\square$ 128 degrees

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Problem 795

17. If converses $\sin \theta=0.14$ , find the value of $\theta$
A 10 B. $37^{\circ}$
C $48^{\circ}$ D. $59^{\circ}$

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Problem 796

$34 \sin (x+5.793) = 34 \left( \cos \square \right)$
Hello there! It seems we have a math problem involving the verification of a trigonometric identity using the sum formula for sine. However, it looks like there is some missing information. Could you provide the result from part (a) or any specific details you have for this problem? This will help me guide you through the solution effectively.
34 \sin(x + 0.493)

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Problem 797

(a) Write the given expression in the form $k \sin (x+\alpha)$ for $0 \leq \alpha<2 \pi$ . Round $\alpha$ to 3 decimal places. Do not round any intermediate calculatio $30 \sin x-16 \cos x \approx 34 \sin (x+0.493)$

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Problem 798

Convert to radians
1. $-270^{\circ}$
2. $-180^{\circ}$
5. $-\frac{\Omega}{4}$ radians $45^{\circ}$ to ralians
3. $\frac{5 \pi}{6}$ radians
4. $\frac{7 \sqrt{4}}{4}$ radians
6. $-\frac{11 \Omega}{18}$ radians
5. - $-\frac{1}{4}$ radians
7. $\frac{2 \pi}{9}$ radians

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Problem 799

Fill in the blank to complete the trigonometric identity. $\sin (-u)=$

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Problem 800

Write the expression as a single trigonometric function. $\sin 9 x \cos 8 x+\cos 9 x \sin 8 x$ $\square$ Submit Answer 12. [-/1 Points] DETAILS MY NOTES MCKTRIC
Write the expression as a single trigonometric function. $\cos 3 x \cos x-\sin 3 x \sin x$ $\square$ Need Help? Watch It Submit Answer 13. [-/1 Points] DETAILS MY NOTES MCKTRIG
Write the expression as a single trigonometric function. $\sin 3 x \cos x-\cos 3 x \sin x$ $\square$

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Trigonometry

Problem 701

If cos⁡2xsin⁡4x=A+Bcos⁡2x+Ccos⁡4x+Dcos⁡2xcos⁡4x\cos ^{2} x \sin ^{4} x=A+B \cos 2 x+C \cos 4 x+D \cos 2 x \cos 4 xcos2xsin4x=A+Bcos2x+Ccos4x+Dcos2xcos4x then A=A=A= B=B=B= C=C=C= D=D=D=

Problem 702

Find the reference angle for 24∘24^{\circ}24∘.

Problem 703

Problem 704

1. Find the exact value of the expression cos⁡(π)⋅cos⁡(3π4)+sin⁡(π)⋅sin⁡(3π4)\cos (\pi) \cdot \cos \left(\frac{3 \pi}{4}\right)+\sin (\pi) \cdot \sin \left(\frac{3 \pi}{4}\right)cos(π)⋅cos(43π​)+sin(π)⋅sin(43π​).

Problem 705

Problem 706

sin⁡−1(−12)\sin ^{-1}\left(-\frac{1}{2}\right)sin−1(−21​)

Problem 707

cos⁡−1(−22)\cos ^{-1}\left(-\frac{\sqrt{2}}{2}\right)cos−1(−22​​)

Problem 708

arccos⁡12\arccos \frac{1}{2}arccos21​

Problem 709

tan⁡−1(−1)\tan ^{-1}(-1)tan−1(−1)

Problem 710

Find the exact values of rrr and yyy given B=76∘B=76^{\circ}B=76∘, and x=6x=6x=6. NOTE: You will need to use trigonometric functions in your answers. r=r=r= □\square□ B=76∘B=76^{\circ}B=76∘ y=y=y=

Problem 711

Problem 712

2cos⁡x+1=0,−π≤x≤2π2 \cos x+1=0,-\pi \leq x \leq 2 \pi2cosx+1=0,−π≤x≤2π

Problem 713

Problem 714

5. Prove the following identities a) cos⁡(β)+tan⁡(β)sin⁡(β)=sec⁡(β)\cos (\beta)+\tan (\beta) \sin (\beta)=\sec (\beta)cos(β)+tan(β)sin(β)=sec(β)

Problem 715

Problem 716

5) cos⁡θsec⁡θ−sin⁡θcot⁡θ=cos⁡θcot⁡θ−tan⁡θcsc⁡θ\frac{\cos \theta}{\sec \theta}-\frac{\sin \theta}{\cot \theta}=\frac{\cos \theta \cot \theta-\tan \theta}{\csc \theta}secθcosθ​−cotθsinθ​=cscθcosθcotθ−tanθ​

Problem 717

csc⁡2(x)−csc⁡(x)cot⁡(x)=11+cos⁡(x)\csc ^{2}(x)-\csc (x) \cot (x)=\frac{1}{1+\cos (x)}csc2(x)−csc(x)cot(x)=1+cos(x)1​

Problem 718

18. The graph of y=2sin⁡b(x−c)+1y=2 \sin b(x-c)+1y=2sinb(x−c)+1 is shown below. Determine a value of ccc. A. 2π7\frac{2 \pi}{7}72π​ C. 2 B. π4\frac{\pi}{4}4π​ D. 2π2\frac{2 \pi}{2}22π​

Problem 719

Find the amplitude of the sinusoidal function.Simplify any fractions. amplitude === □\square□

Problem 720

sin⁡(θ)+11−sin⁡(θ)=(tan⁡(θ)+sec⁡(θ))2\frac{\sin (\theta)+1}{1-\sin (\theta)}=(\tan (\theta)+\sec (\theta))^{2}1−sin(θ)sin(θ)+1​=(tan(θ)+sec(θ))2

Problem 721

Problem 722

Problem 723

Problem 724

Problem 725

Problem 726

Find the cosine of ∠G\angle G∠G.Write your answer in simplified, rationalized form. Do not round. cos⁡(G)=\cos (G)=cos(G)=

Problem 727

The accompanying graph shows a sinusoidal function. Complete parts a) through c) below. a) What is the period of this function?The period is □\square□

Problem 728

Prove this Idenity is true 1+cos⁡2xsin⁡2x=cot⁡x\frac{1+\cos 2 x}{\sin 2 x}=\cot xsin2x1+cos2x​=cotx

Problem 729

Problem 730

Question 9 10 ptsFind the exact value of 2cos⁡(15∘)sin⁡(15∘)2 \cos \left(15^{\circ}\right) \sin \left(15^{\circ}\right)2cos(15∘)sin(15∘) 12\frac{1}{2}21​ 1 30 32\frac{\sqrt{3}}{2}23​​

Problem 731

Consider the following. t=5π3t=\frac{5 \pi}{3}t=35π​ (a) Find the reference number tˉ\bar{t}tˉ for the value of ttt. tˉ=π3\bar{t}=\frac{\pi}{3}tˉ=3π​ (b) Find the terminal point determined by ttt. (x,y)=(□)(x, y)=(\square)(x,y)=(□) Need Help? Read It

Problem 732

B=75∘,c=4,a=3B=75^{\circ}, c=4, a=3B=75∘,c=4,a=3 w window) 3 Points b=□C=□A=□\begin{array}{l} b=\square \\ C=\square \\ A=\square \end{array}b=□C=□A=□​

Problem 733

Score: 6/10Find the exact value of sin⁡135∘\sin 135^{\circ}sin135∘Answer

Problem 734

Use a calculator to evaluate arcsin( 0.55 ) to 4 decimal places in radian

Problem 735

Use a calculator to evaluate tan⁡−1(51)\tan ^{-1}(51)tan−1(51) to 2 decimal places in degrees. If necessary, use 3.1416 as an approximation to pi.

Problem 736

Problem 737

cos⁡(x+π6)=22\cos \left(x+\frac{\pi}{6}\right)=\frac{\sqrt{2}}{2}cos(x+6π​)=22​​ a. Set for general solution6. Set on the interval [0,2π)[0,2 \pi)[0,2π)

Problem 738

Find measures of a positive angle and a negative angle coterminal with −29π5-\frac{29 \pi}{5}−529π​ radians and distinct from it.Give the answers in simplest form. positive angle = □\square□ radians negative angle === □\square□ radians

Problem 739

View Policies Show Attempt HistoryCurrent Attempt in ProgressYour answer is incorrect.In which quadrant is a point with the polar coordinate θ=2.1π\theta=2.1 \piθ=2.1π ?Quadrant II eTextbook and MediaHintSave for Later Attempts: 1 of 3 used Submit Answer

Problem 740

What is the correct equation for the following function? y=cos⁡2xy=\cos 2 xy=cos2x y=12cos⁡xy=\frac{1}{2} \cos xy=21​cosx y=2cos⁡xy=2 \cos xy=2cosx y=cos⁡12xy=\cos \frac{1}{2} xy=cos21​x

Problem 741

Problem 742

Use the sum or difference formula for cosine to find the exact value for cos⁡(105∘)\cos \left(105^{\circ}\right)cos(105∘) cos⁡(105∘)=\cos \left(105^{\circ}\right)=cos(105∘)=

Problem 743

Use a compound angle formula to determine the exact value of tan⁡π12\tan \frac{\pi}{12}tan12π​

Problem 744

Using the Law of Sines to solve the all possible triangles if ∠A=119∘,a=30,b=19\angle A=119^{\circ}, a=30, b=19∠A=119∘,a=30,b=19. If no answer exists, enter DNE for all answers. ∠B\angle B∠B is □\square□ degrees; ∠C\angle C∠C is □\square□ degrees; c=□;c=\square ;c=□;

Problem 745

Problem 746

Use half angle formula (sin⁡(2x))4=(\sin (2 x))^{4}=(sin(2x))4=

Problem 747

If $\cos ^{2} x \sin ^{4} x=A+B \cos 2 x+C \cos 4 x+D \cos 2 x \cos 4 x$ then $A=$ $B=$ $C=$ $D=$

Find the reference angle for $24^{\circ}$ .

1. Find the exact value of the expression $\cos (\pi) \cdot \cos \left(\frac{3 \pi}{4}\right)+\sin (\pi) \cdot \sin \left(\frac{3 \pi}{4}\right)$ .

$\sin ^{-1}\left(-\frac{1}{2}\right)$

$\cos ^{-1}\left(-\frac{\sqrt{2}}{2}\right)$

$\arccos \frac{1}{2}$

$\tan ^{-1}(-1)$

Find the exact values of $r$ and $y$ given $B=76^{\circ}$ , and $x=6$ . NOTE: You will need to use trigonometric functions in your answers. $r=$ $\square$ $B=76^{\circ}$ $y=$

$2 \cos x+1=0,-\pi \leq x \leq 2 \pi$

5. Prove the following identities a) $\cos (\beta)+\tan (\beta) \sin (\beta)=\sec (\beta)$

5) $\frac{\cos \theta}{\sec \theta}-\frac{\sin \theta}{\cot \theta}=\frac{\cos \theta \cot \theta-\tan \theta}{\csc \theta}$

$\csc ^{2}(x)-\csc (x) \cot (x)=\frac{1}{1+\cos (x)}$

18. The graph of $y=2 \sin b(x-c)+1$ is shown below. Determine a value of $c$ . A. $\frac{2 \pi}{7}$ C. 2 B. $\frac{\pi}{4}$ D. $\frac{2 \pi}{2}$

Find the amplitude of the sinusoidal function.
Simplify any fractions. amplitude $=$ $\square$

$\frac{\sin (\theta)+1}{1-\sin (\theta)}=(\tan (\theta)+\sec (\theta))^{2}$

Find the cosine of $\angle G$ .
Write your answer in simplified, rationalized form. Do not round. $\cos (G)=$

The accompanying graph shows a sinusoidal function. Complete parts a) through c) below. a) What is the period of this function?
The period is $\square$

Prove this Idenity is true $\frac{1+\cos 2 x}{\sin 2 x}=\cot x$

Question 9 10 pts
Find the exact value of $2 \cos \left(15^{\circ}\right) \sin \left(15^{\circ}\right)$ $\frac{1}{2}$ 1 30 $\frac{\sqrt{3}}{2}$

Consider the following. $t=\frac{5 \pi}{3}$ (a) Find the reference number $\bar{t}$ for the value of $t$ . $\bar{t}=\frac{\pi}{3}$ (b) Find the terminal point determined by $t$ . $(x, y)=(\square)$ Need Help? Read It

$B=75^{\circ}, c=4, a=3$ w window) 3 Points $\begin{array}{l} b=\square \\ C=\square \\ A=\square \end{array}$

Score: 6/10
Find the exact value of $\sin 135^{\circ}$
Answer

Use a calculator to evaluate $\tan ^{-1}(51)$ to 2 decimal places in degrees. If necessary, use 3.1416 as an approximation to pi.

$\cos \left(x+\frac{\pi}{6}\right)=\frac{\sqrt{2}}{2}$ a. Set for general solution
6. Set on the interval $[0,2 \pi)$

Find measures of a positive angle and a negative angle coterminal with $-\frac{29 \pi}{5}$ radians and distinct from it.
Give the answers in simplest form. positive angle = $\square$ radians negative angle $=$ $\square$ radians

View Policies Show Attempt History
Current Attempt in Progress
Your answer is incorrect.
In which quadrant is a point with the polar coordinate $\theta=2.1 \pi$ ?
Quadrant II eTextbook and Media
Hint
Save for Later Attempts: 1 of 3 used Submit Answer

What is the correct equation for the following function? $y=\cos 2 x$ $y=\frac{1}{2} \cos x$ $y=2 \cos x$ $y=\cos \frac{1}{2} x$

Use the sum or difference formula for cosine to find the exact value for $\cos \left(105^{\circ}\right)$ $\cos \left(105^{\circ}\right)=$

Use a compound angle formula to determine the exact value of $\tan \frac{\pi}{12}$

Using the Law of Sines to solve the all possible triangles if $\angle A=119^{\circ}, a=30, b=19$ . If no answer exists, enter DNE for all answers. $\angle B$ is $\square$ degrees; $\angle C$ is $\square$ degrees; $c=\square ;$

Use half angle formula $(\sin (2 x))^{4}=$

Find two positive and two negative angles coterminal with $A = -630^{\circ}$ .

Convert the angle $-51^{\circ} 30^{\prime}$ to decimal degree notation.

Convert the angle $-75^{\circ} 3^{\prime}$ to decimal degrees.

Convert the angle $-41^{\circ} 54^{\prime}$ to decimal degrees.

Calculate $\cos 48^{\circ}$ and round to two decimal places. Options: A. 0.50 B. 1 C. 0.67 D. 0.48 E. None.

A train track rises at $10^{\circ}$ . How high does it rise over 230 feet? Estimate to two decimal places. A. 121.34 in B. 45.85 ft C. 40.56 ft D. 115.36 in E. None.

Find the legs of a right triangle with an angle of $65^{\circ}$ and a hypotenuse of 12. Round to two decimals.

Simplify $\tan 100^{\circ} + 4 \sin 100^{\circ}$ .

Find $\tan B$ given $a=5$ , $b=12$ , and $c=13$ . Also, $\sin B=\frac{12}{13}$ , $\cos B=\frac{5}{13}$ .

Find side $c$ with $a=5$ , $b=12$ . Then calculate $\sin B$ and simplify the results.

Given sides $a=5$ and $b=12$ , find $c$ , $\sin B$ , $\cos B$ , $\tan B$ , and $\sec B$ .

Find the trigonometric functions for angle B given $a=5$ , $b=12$ , $c=13$ : $\sin B$ , $\cos B$ , $\tan B$ , $\sec B$ , $\csc B$ .

Find the value of $\csc 45^{\circ}$ . Simplify your answer with integers or fractions.

Rewrite $\sin 61^{\circ}$ using its cofunction. What is $\sin 61^{\circ}=$ ? (Provide the answer without the degree symbol.)

Rewrite $\tan 38^{\circ}$ using its cofunction. What is the simplified answer?

Calculate the exact value of $\sec 30^{\circ}$ . Simplify your answer with integers or fractions.

Find the exact value of $\sin 60^{\circ}$ . Simplify your answer with radicals, integers, or fractions.

Find the exact value of $\tan 30^{\circ}$ . Simplify your answer with integers or fractions.

Rewrite $\tan 74^{\circ}$ using its cofunction. What is $\tan 74^{\circ}=$ ? Simplify your answer without the degree symbol.

Calculate the exact value of $\csc 45^{\circ}$ . Simplify your answer using integers or fractions.

Find the smallest positive angle (in degrees) coterminal with $A=247^{\circ}$ .

Find $\theta$ using the equation $\cos \theta=\frac{5}{12}$ . Round to the nearest degree if necessary.

A building casts a 130 ft shadow with the Sun at an $82.9^{\circ}$ angle. Find the building's height.

Kristen's telescope is 5 ft high. At an $8^{\circ}$ angle, how tall is the tree 120 ft away?