Unit Circle & Radians

Problem 301

Find the values of sint,cost,tant,csct,sect\sin \mathrm{t}, \cos \mathrm{t}, \tan \mathrm{t}, \boldsymbol{\operatorname { c s c }} \mathrm{t}, \boldsymbol{\operatorname { s e c }} \mathrm{t}, and cott\cot \mathrm{t} if (22,22)\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right) is the point on the unit circle that corresponds to the real number t .

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Problem 302

Convert each degree measure into radians. 675-675^{\circ}

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Problem 303

Find the exact value of sin16π3\sin \frac{16 \pi}{3} using the periodic properties of trigonometric functions.

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Problem 304

Calculate the value of csc(7π2)sec(8π3)\csc \left(\frac{7 \pi}{2}\right) - \sec \left(\frac{8 \pi}{3}\right) without a calculator.

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Problem 305

Find the value of cos1(sin7π6)\cos^{-1}\left(\sin \frac{7\pi}{6}\right).

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Problem 306

Calculate the value of cos(3π)+sin(3π2)\cos (-3 \pi) + \sin \left(\frac{3 \pi}{2}\right) without a calculator.

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Problem 307

Calculate the value of \tan \left(\frac{-9 \pi}{4}\right)-\cos \left(\frac{-9 \pi}{4}\right} without a calculator.

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Problem 308

Calculate \tan \left(\frac{-9 \pi}{4}\right) - \cos \left(\frac{-9 \pi}{4}\right} without a calculator.

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Problem 309

Given the reference angle t=90t=90^{\circ} find the measure of θ\theta in standard position if its terminal side lies in: (a) quadrant I: \square (b) quadrant II: \square (c) quadrant III: \square (d) quadrant IV: \square Check Answer

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Problem 310

Answer the following. (a) Find an angle between 0 and 2π2 \pi that is coterminal with 11π5\frac{11 \pi}{5}. (b) Find an angle between 00^{\circ} and 360360^{\circ} that is coterminal with 815815^{\circ}.
Give exact values for your answers. (a) Ifradians π\pi (b) \square^{\circ}

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Problem 311

0. Using a calculator, determine the solutions for each equation, to two decimal places, on the interval 0x2π0 \leq x \leq 2 \pi. a) sin2x=12\sin 2 x=\frac{1}{\sqrt{2}} c) sin3x=32\sin 3 x=-\frac{\sqrt{3}}{2} e) cos2x=12\cos 2 x=-\frac{1}{2} b) sin4x=12\sin 4 x=\frac{1}{2} d) cos4x=12\cos 4 x=-\frac{1}{\sqrt{2}} f) cosx2=32\cos \frac{x}{2}=\frac{\sqrt{3}}{2}

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Problem 312

11. Evaluate the following exactly. a) cos(25π12)\cos \left(\frac{25 \pi}{12}\right) b) sin(19π12)\sin \left(\frac{19 \pi}{12}\right)

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Problem 313

π2θπ2-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}. Find the value of θ\theta in radians. sin(θ)=12\sin (\theta)=\frac{1}{2}
Write your answer in simplified, rationalized form. Do not round. θ=\theta= \square

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Problem 314

A vector with magnitude 4 points in a direction 295 degrees counterclockwise from the positive xx axis. Write the vector in component form. Vector == \square Give each value accurate to at least 1 decimal place Add Work
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Problem 315

Select the correct answer.
Convert θ=3π4\theta=\frac{3 \pi}{4} to rectangular form. A. y=1y=-1 B. y=1y=1 C. y=xy=x D. y=xy=-x E. x=1x=-1

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Problem 316

Find all θ\theta in [0,360)[0^{\circ}, 360^{\circ}) such that cosθ=22\cos \theta=\frac{\sqrt{2}}{2}.

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Problem 317

9. Which quadrant does θ\theta lie in if sinθ<0\sin \theta<0 and tanθ>0\tan \theta>0 ? A. I B. II C. III D. IV

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Problem 318

Given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function. cos60\cos 60^{\circ}

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Problem 319

8. Determine the exact value of each trigonometric ratio. a) sin4π3\sin \frac{4 \pi}{3} b) cos300\cos 300^{\circ} c) tan(570)\tan \left(-570^{\circ}\right) d) csc135\csc 135^{\circ} e) sec(3π2)\sec \left(-\frac{3 \pi}{2}\right) f) cot23π6\cot \frac{23 \pi}{6}

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Problem 320

For the rotation 71π8-\frac{71 \pi}{8}, find the coterminal angle from 0θ<2π0 \leq \theta<2 \pi, the quadrant, and the reference angle.

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Problem 321

Find the second least positive value (in radians) for β\beta given 11π/611\pi/6 and for γ\gamma given tan(γ)=1\tan(\gamma)=1.

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Problem 322

If tan(γ)=1\tan (\gamma)=1, what are the least and second least positive values of γ\gamma in radians?

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