Unit Circle & Radians

Problem 1

错误的命题是哪个？A. 角的度量单位不同 B. $1^{\circ}$ 是周角的 $\frac{1}{360}$ C. $1 \mathrm{rad}$ 大于 $1^{\circ}$ D. 弧度与半径有关

See Solution

Problem 2

The smallest positive co-terminal angle for $55^{\circ}$ is

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Problem 3

Convert these angles from radians to degrees: (a) $3 \pi$ , (b) $\frac{2 \pi}{3}$ , (c) $\frac{\pi}{8}$ , (d) $\frac{\pi}{5}$ , (e) $\frac{3 \pi}{4}$ .

See Solution

Problem 4

Find the values of: (a) $\sin \frac{\pi}{3}$ , (b) $\cos \frac{2 \pi}{3}$ , and $\tan \frac{7 \pi}{4}$ in surd form.

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Problem 5

Convert these angles to radians as multiples of $\pi$ : (a) $60^{\circ}$ , (b) $120^{\circ}$ , (c) $720^{\circ}$ , (d) $15^{\circ}$ , (e) $190^{\circ}$ .

See Solution

Problem 6

Find the sine, cosine, and tangent of angle $\theta$ at point $(-9,4)$ on a circle. Provide exact values only.

See Solution

Problem 7

Find the primary trigonometric ratios for $\theta = 2$ radians at the point $(-9,4)$ on the circle's circumference.

See Solution

Problem 8

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

See Solution

Problem 9

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

See Solution

Problem 10

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

See Solution

Problem 11

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

See Solution

Problem 12

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

See Solution

Problem 13

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

See Solution

Problem 14

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

See Solution

Problem 15

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

See Solution

Problem 16

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

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Problem 17

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

See Solution

Problem 18

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

See Solution

Problem 19

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

See Solution

Problem 20

Find the smallest positive angle (in degrees) coterminal with $A = 142^{\circ}$ .

See Solution

Problem 21

Find two positive and two negative angles coterminal with the angle $A=90^{\circ}$ .

See Solution

Problem 22

Determine the quadrants for angle $\theta$ where $\cos \theta > 0$ and $\sin \theta < 0$ .

See Solution

Problem 23

Find the six trigonometric functions for the angle $765^{\circ}$ . Calculate $\sin 765^{\circ}=$ (simplify and rationalize).

See Solution

Problem 24

Find the exact value of $\sin 1935^{\circ}$ . Simplify your answer using integers or fractions.

See Solution

Problem 25

Find the exact value of $\sin(-855^\circ)$ . Simplify your answer, using integers or fractions.

See Solution

Problem 26

Find the exact value of $\sin 2100^{\circ}$ . Simplify your answer, including radicals, using integers or fractions.

See Solution

Problem 27

Find the six trigonometric functions for the angle $-870^{\circ}$ . Simplify your answer, including any radicals.

See Solution

Problem 28

Find the smallest positive angle (in degrees) that is coterminal with $A = -7^{\circ}$ .

See Solution

Problem 29

If $\sin \theta=\frac{2}{5}$ , which quadrants could the angle $\theta$ be in? Check all that apply: Quadrant 1, 2, 3, 4.

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Problem 30

Find the six trigonometric functions for the angle $-\frac{5 \pi}{4}$ without using a calculator.

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Problem 31

Find the values of the six trigonometric functions for the angle $\frac{\pi}{4}$ without using a calculator.

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Problem 32

Find the exact value of $\sin(13 \pi)$ without using a calculator.

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Problem 33

Find the exact value of $\cos (-2 \pi)$ without using a calculator.

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Problem 34

Find the six trigonometric functions for the angle $\frac{3 \pi}{4}$ . State "not defined" if applicable.

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Problem 35

Find the exact values of the six trigonometric functions of $t$ for the point $P=\left(\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right)$ on the unit circle.

See Solution

Problem 36

Find the value of $\cot \frac{3 \pi}{2} + \cos \frac{3 \pi}{2}$ without a calculator.

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Problem 37

Omar needs to find $\cos \left(-\frac{2 \pi}{3}\right)$ . Use the reference angle and quadrant info to solve.

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Problem 38

Find the exact value of $\cos \left(-\frac{\pi}{3}\right)$ using reference angles.

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Problem 39

Find the values of the trigonometric functions given that $\sin \theta=1$ . What is $\cos \theta$ ? A. $\cos \theta=$ B. Undefined.

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Problem 40

Find the six trigonometric functions of $t$ for the point $\left(-\frac{\sqrt{3}}{5},-\frac{\sqrt{22}}{5}\right)$ on the unit circle.

See Solution

Problem 41

Find the six trigonometric functions for the point $\left(-\frac{1}{\sqrt{26}},-\frac{5}{\sqrt{26}}\right)$ on the unit circle.

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Problem 42

Find the six trigonometric functions for the point $\left(-\frac{1}{\sqrt{26}},-\frac{5}{\sqrt{26}}\right)$ on the unit circle.

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Problem 43

Find the acute angle $\theta$ where $\sin \theta = \frac{\sqrt{3}}{2}$ . What is $\theta$ in radians?

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Problem 44

Find the angle $\alpha$ coterminal with $\theta=\frac{\pi}{14}$ in the range $-2\pi < \alpha < 0$ .

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Problem 45

Solve $\cos \left(\frac{x}{2}\right)=-\frac{\sqrt{3}}{2}$ for $x$ in $[0,2\pi)$ . Provide exact radian solutions.

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Problem 46

Find the value of $\sin ^{-1}\left[\sin \left(-\frac{7 \pi}{6}\right)\right]$ without a calculator.

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Problem 47

Find the family of special angles for $\theta = \frac{14 \pi}{3}$ and its least nonnegative coterminal angle $\theta_{c}$ .

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Problem 48

Identify the family of special angles for $-\frac{43 \pi}{6}$ and find the least nonnegative coterminal angle $\theta_{c}$ .

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Problem 49

Find the exact value of $\sin \left(-\frac{9 \pi}{2}\right)$ and answer parts a, b, c, and d. Where is the terminal side of $\theta=-\frac{9 \pi}{2}$ ?

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Problem 50

Find $\cot(-12\pi)$ exactly. Answer parts a, b, c, and d: a. Where is the terminal side of $\theta = -12\pi$ ?

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Problem 51

Find $\cot (-12 \pi)$ without a calculator. a. Where is the terminal side of $\theta=-12 \pi$ ? b. Give the coordinates on the terminal side with $r=1$ .

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Problem 52

Find $\cot (-12 \pi)$ by answering: a) Where is $\theta=-12 \pi$ ? b) Coordinates for $r=1$ . c) $\cot \theta$ definition?

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Problem 53

Find $\cot(-12\pi)$ : a. Where is $\theta=-12\pi$ ? b. Coordinates on terminal side? c. What is $\cot \theta$ ?

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Problem 54

Find the value of $\tan(-7 \pi)$ and answer: a. Where is the terminal side of $\theta=-7 \pi$ ?

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Problem 55

Find the reference angle for $\theta=\frac{9 \pi}{4}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

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Problem 56

Find the reference angle for $\theta=\frac{29 \pi}{6}$ and the least nonnegative angle coterminal with it. $\theta_{\mathrm{C}}=$

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Problem 57

Find the reference angle for $\theta=\frac{29 \pi}{6}$ and the least nonnegative angle coterminal with it. What quadrant is it in?

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Problem 58

Find the reference angle for $\theta=\frac{29 \pi}{6}$ and the least nonnegative coterminal angle. What is $\theta_{\mathrm{R}}$ ?

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Problem 59

Find the reference angle for $\theta = -\frac{17 \pi}{4}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}} =$

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Problem 60

Find the reference angle for $\theta=-\frac{29 \pi}{6}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

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Problem 61

Find the reference angle for $\theta=-\frac{29 \pi}{6}$ and the least nonnegative coterminal angle $\theta_{C}$ .

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Problem 62

Find the reference angle for $\theta=\frac{48 \pi}{18}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

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Problem 63

Find the reference angle for $\theta=\frac{48 \pi}{18}$ and the least nonnegative coterminal angle $\theta_{C}=\frac{2 \pi}{3}$ . In which quadrant is $\theta_{C}$ ?

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Problem 64

Find the reference angle for $\theta=\frac{48 \pi}{18}$ and the angle $\theta_{C}=\frac{2 \pi}{3}$ . What is $\theta_{R}$ ?

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Problem 65

Find the reference angle for $\theta=\frac{31 \pi}{12}$ . Also, find the least nonnegative angle coterminal with $\theta$ . $\theta_{C}=$

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Problem 66

Find the reference angle for $\theta=\frac{31 \pi}{12}$ and the least nonnegative coterminal angle $\theta_{C}$ . What quadrant is $\theta_{C}$ in?

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Problem 67

Find the reference angle for $\theta=\frac{31 \pi}{12}$ and the coterminal angle $\theta_{C}=\frac{7 \pi}{12}$ . What is $\theta_{R}$ ?

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Problem 68

Find the reference angle for $\theta=-\frac{29 \pi}{12}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

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Problem 69

Find the reference angle for $\theta=570^{\circ}$ and the least nonnegative coterminal angle $\theta_{C}$ .

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Problem 70

Find the reference angle for $\theta=-\frac{29 \pi}{12}$ and the coterminal angle $\theta_{C}=\frac{19 \pi}{12}$ in quadrant IV. What is $\theta_{R}$ ?

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Problem 71

Find the reference angle for $\theta=570^{\circ}$ and the least nonnegative coterminal angle $\theta_{C}$ . What quadrant is $\theta_{C}$ in?

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Problem 72

Find the reference angle for $\theta=570^{\circ}$ and the angle $\theta_{C}=210^{\circ}$ in quadrant III. What is $\theta_{R}=\square^{\circ}$ ?

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Problem 73

Find the reference angle for $\theta=-420^{\circ}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

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Problem 74

Find the reference angle for $\theta=-420^{\circ}$ and the least nonnegative coterminal angle. Which quadrant is $\theta_{C}=300^{\circ}$ in?

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Problem 75

Find the reference angle for $\theta=-420^{\circ}$ and the least nonnegative coterminal angle. What is $\theta_{R}$ ?

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Problem 76

Find $\tan \left(\frac{7 \pi}{6}\right)$ without a calculator. Answer: (a) Which quadrant is $\theta=\frac{7 \pi}{6}$ in?

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Problem 77

Find the exact value of $\tan \left(\frac{7 \pi}{4}\right)$ and answer: a. Which quadrant is it in? b. Is tangent positive or negative?

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Problem 78

Find the value of $\tan \left(\frac{7 \pi}{4}\right)$ by answering: a. Which quadrant? b. Is tangent positive or negative? c. Reference angle?

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Problem 79

Find the value of $\tan \left(\frac{7 \pi}{4}\right)$ . What is the reference angle and its equivalent expression?

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Problem 80

Find the value of $\sin \left(-\frac{4 \pi}{3}\right)$ . In which quadrant is the angle $\theta=-\frac{4 \pi}{3}$ ?

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Problem 81

Find the exact value of $\csc \left(-\frac{7 \pi}{6}\right)$ and answer: (a) Which quadrant? (b) Is cosecant positive or negative?

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Problem 82

Find the value of $\sin \left(-\frac{4 \pi}{3}\right)$ .
d. Which is equivalent: A. $\sin \frac{\pi}{3}$ B. $-\sin \frac{\pi}{6}$ C. $-\sin \frac{\pi}{3}$ D. $\sin \frac{\pi}{6}$
e. Calculate $\sin \left(-\frac{4 \pi}{3}\right)=\ldots$ (simplify).

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Problem 83

Find the exact value of $\sin \left(-\frac{4 \pi}{3}\right)$ . Reference angle is $\theta_{R}=\frac{\pi}{3}$ . Which expression is equivalent: A. $\sin \frac{\pi}{3}$ , B. $-\sin \frac{\pi}{6}$ , C. $-\sin \frac{\pi}{3}$ , D. $\sin \frac{\pi}{6}$ ?

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Problem 84

Determine the quadrant of $\theta = -\frac{7 \pi}{6}$ and find $\csc \left(-\frac{7 \pi}{6}\right)$ .

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Problem 85

Find $\sin \left(-\frac{4 \pi}{3}\right)$ by answering: a) Which quadrant is $\theta=-\frac{4 \pi}{3}$ in? b) Is sine positive or negative? c) What is the reference angle?

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Problem 86

Find $\cot \left(-\frac{5 \pi}{4}\right)$ without a calculator. Identify the quadrant, sign, and reference angle $\theta_{\mathrm{R}}$ .

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Problem 87

Find $\cos \left(\frac{23 \pi}{6}\right)$ and identify the quadrant of $\theta=\frac{23 \pi}{6}$ .

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Problem 88

Find $\tan \left(\frac{17 \pi}{6}\right)$ without a calculator. Which quadrant is $\theta=\frac{17 \pi}{6}$ in?

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Problem 89

Find $\cos \left(\frac{23 \pi}{6}\right)$ without a calculator. In which quadrant does $\theta=\frac{23 \pi}{6}$ lie?

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Problem 90

Find $\tan \left(\frac{17 \pi}{6}\right)$ . Which quadrant is it in? Reference angle? Equivalent expression?

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Problem 91

Find $\cos \left(\frac{23 \pi}{6}\right)$ without a calculator. Which quadrant is $\theta=\frac{23 \pi}{6}$ in? What is the reference angle? $\theta_{R}=$

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Problem 92

Find the reference angle for a rotation of $212^{\circ}$ .

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Problem 93

Find the value of $\sin \left(\frac{10 \pi}{3}\right)$ and the quadrant of angle $\theta=\frac{10 \pi}{3}$ .

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Problem 94

Find the exact value of $\sin \left(\frac{10 \pi}{3}\right)$ . What quadrant is $\theta=\frac{10 \pi}{3}$ in? Reference angle? $\theta_{\mathrm{R}}=$

See Solution

Problem 95

Find $\csc \left(\frac{8 \pi}{3}\right)$ and identify the quadrant of $\theta=\frac{8 \pi}{3}$ .

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Problem 96

Find $\csc \left(\frac{8 \pi}{3}\right)$ without a calculator. Where's the angle's quadrant? What's the reference angle? Choose the equivalent expression.

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Problem 97

Find the value of $\csc \left(\frac{8 \pi}{3}\right)$ without a calculator. What quadrant is $\theta=\frac{8 \pi}{3}$ in? What is the reference angle? $\theta_{\mathrm{R}}=$

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Problem 98

The angle $\theta=-\frac{17 \pi}{6}$ is in which quadrant?

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Problem 99

Find the value of $\tan \left(-\frac{19 \pi}{6}\right)$ .
(a) Which quadrant is $\theta=-\frac{19 \pi}{6}$ in? (b) Is tangent positive or negative there? (c) What is the reference angle $\theta_{R}=$ ?

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Problem 100

The terminal side of the angle $\theta=-\frac{11 \pi}{4}$ lies in which quadrant?

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Unit Circle & Radians

Problem 1

错误的命题是哪个？A. 角的度量单位不同 B. 1∘1^{\circ}1∘ 是周角的 1360\frac{1}{360}3601​ C. 1rad1 \mathrm{rad}1rad 大于 1∘1^{\circ}1∘ D. 弧度与半径有关

Problem 2

The smallest positive co-terminal angle for 55∘55^{\circ}55∘ is

Problem 3

Convert these angles from radians to degrees: (a) 3π3 \pi3π, (b) 2π3\frac{2 \pi}{3}32π​, (c) π8\frac{\pi}{8}8π​, (d) π5\frac{\pi}{5}5π​, (e) 3π4\frac{3 \pi}{4}43π​.

Problem 4

Find the values of: (a) sin⁡π3\sin \frac{\pi}{3}sin3π​, (b) cos⁡2π3\cos \frac{2 \pi}{3}cos32π​, and tan⁡7π4\tan \frac{7 \pi}{4}tan47π​ in surd form.

Problem 5

Convert these angles to radians as multiples of π\piπ: (a) 60∘60^{\circ}60∘, (b) 120∘120^{\circ}120∘, (c) 720∘720^{\circ}720∘, (d) 15∘15^{\circ}15∘, (e) 190∘190^{\circ}190∘.

Problem 6

Find the sine, cosine, and tangent of angle θ\thetaθ at point (−9,4)(-9,4)(−9,4) on a circle. Provide exact values only.

Problem 7

Find the primary trigonometric ratios for θ=2\theta = 2θ=2 radians at the point (−9,4)(-9,4)(−9,4) on the circle's circumference.

Problem 8

Calculate tg⁡11π6\operatorname{tg} \frac{11 \pi}{6}tg611π​.

Problem 9

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

Problem 10

Find the quadrant(s) where sin⁡α<0\sin \alpha<0sinα<0 and sec⁡α<0\sec \alpha<0secα<0. Answer as 1,2,31,2,31,2,3, or 4, separated by commas.

Problem 11

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

Problem 12

Find the exact value of sin⁡60∘\sin 60^{\circ}sin60∘. Simplify your answer with radicals, integers, or fractions.

Problem 13

Find the exact value of tan⁡30∘\tan 30^{\circ}tan30∘. Simplify your answer with integers or fractions.

Problem 14

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

Problem 15

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

Problem 16

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

Problem 17

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

Problem 18

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

Problem 19

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

Problem 20

Find the smallest positive angle (in degrees) coterminal with A=142∘A = 142^{\circ}A=142∘.

Problem 21

Find two positive and two negative angles coterminal with the angle A=90∘A=90^{\circ}A=90∘.

Problem 22

Determine the quadrants for angle θ\thetaθ where cos⁡θ>0\cos \theta > 0cosθ>0 and sin⁡θ<0\sin \theta < 0sinθ<0.

Problem 23

Find the six trigonometric functions for the angle 765∘765^{\circ}765∘. Calculate sin⁡765∘=\sin 765^{\circ}=sin765∘= (simplify and rationalize).

Problem 24

Find the exact value of sin⁡1935∘\sin 1935^{\circ}sin1935∘. Simplify your answer using integers or fractions.

Problem 25

Find the exact value of sin⁡(−855∘)\sin(-855^\circ)sin(−855∘). Simplify your answer, using integers or fractions.

Problem 26

Find the exact value of sin⁡2100∘\sin 2100^{\circ}sin2100∘. Simplify your answer, including radicals, using integers or fractions.

Problem 27

Find the six trigonometric functions for the angle −870∘-870^{\circ}−870∘. Simplify your answer, including any radicals.

Problem 28

Find the smallest positive angle (in degrees) that is coterminal with A=−7∘A = -7^{\circ}A=−7∘.

Problem 29

If sin⁡θ=25\sin \theta=\frac{2}{5}sinθ=52​, which quadrants could the angle θ\thetaθ be in? Check all that apply: Quadrant 1, 2, 3, 4.

Problem 30

Find the six trigonometric functions for the angle −5π4-\frac{5 \pi}{4}−45π​ without using a calculator.

Problem 31

Find the values of the six trigonometric functions for the angle π4\frac{\pi}{4}4π​ without using a calculator.

Problem 32

Find the exact value of sin⁡(13π)\sin(13 \pi)sin(13π) without using a calculator.

Problem 33

Find the exact value of cos⁡(−2π)\cos (-2 \pi)cos(−2π) without using a calculator.

Problem 34

Find the six trigonometric functions for the angle 3π4\frac{3 \pi}{4}43π​. State "not defined" if applicable.

Problem 35

Find the exact values of the six trigonometric functions of ttt for the point P=(223,−13)P=\left(\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right)P=(322​​,−31​) on the unit circle.

Problem 36

Find the value of cot⁡3π2+cos⁡3π2\cot \frac{3 \pi}{2} + \cos \frac{3 \pi}{2}cot23π​+cos23π​ without a calculator.

Problem 37

Omar needs to find cos⁡(−2π3)\cos \left(-\frac{2 \pi}{3}\right)cos(−32π​). Use the reference angle and quadrant info to solve.

Problem 38

Find the exact value of cos⁡(−π3)\cos \left(-\frac{\pi}{3}\right)cos(−3π​) using reference angles.

Problem 39

Find the values of the trigonometric functions given that sin⁡θ=1\sin \theta=1sinθ=1. What is cos⁡θ\cos \thetacosθ? A. cos⁡θ=\cos \theta=cosθ= B. Undefined.

Problem 40

错误的命题是哪个？A. 角的度量单位不同 B. $1^{\circ}$ 是周角的 $\frac{1}{360}$ C. $1 \mathrm{rad}$ 大于 $1^{\circ}$ D. 弧度与半径有关

The smallest positive co-terminal angle for $55^{\circ}$ is

Convert these angles from radians to degrees: (a) $3 \pi$ , (b) $\frac{2 \pi}{3}$ , (c) $\frac{\pi}{8}$ , (d) $\frac{\pi}{5}$ , (e) $\frac{3 \pi}{4}$ .

Find the values of: (a) $\sin \frac{\pi}{3}$ , (b) $\cos \frac{2 \pi}{3}$ , and $\tan \frac{7 \pi}{4}$ in surd form.

Convert these angles to radians as multiples of $\pi$ : (a) $60^{\circ}$ , (b) $120^{\circ}$ , (c) $720^{\circ}$ , (d) $15^{\circ}$ , (e) $190^{\circ}$ .

Find the sine, cosine, and tangent of angle $\theta$ at point $(-9,4)$ on a circle. Provide exact values only.

Find the primary trigonometric ratios for $\theta = 2$ radians at the point $(-9,4)$ on the circle's circumference.

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

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

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

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

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.

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

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

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

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

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

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

Find the smallest positive angle (in degrees) coterminal with $A = 142^{\circ}$ .

Find two positive and two negative angles coterminal with the angle $A=90^{\circ}$ .

Determine the quadrants for angle $\theta$ where $\cos \theta > 0$ and $\sin \theta < 0$ .

Find the six trigonometric functions for the angle $765^{\circ}$ . Calculate $\sin 765^{\circ}=$ (simplify and rationalize).

Find the exact value of $\sin 1935^{\circ}$ . Simplify your answer using integers or fractions.

Find the exact value of $\sin(-855^\circ)$ . Simplify your answer, using integers or fractions.

Find the exact value of $\sin 2100^{\circ}$ . Simplify your answer, including radicals, using integers or fractions.

Find the six trigonometric functions for the angle $-870^{\circ}$ . Simplify your answer, including any radicals.

Find the smallest positive angle (in degrees) that is coterminal with $A = -7^{\circ}$ .

If $\sin \theta=\frac{2}{5}$ , which quadrants could the angle $\theta$ be in? Check all that apply: Quadrant 1, 2, 3, 4.

Find the six trigonometric functions for the angle $-\frac{5 \pi}{4}$ without using a calculator.

Find the values of the six trigonometric functions for the angle $\frac{\pi}{4}$ without using a calculator.

Find the exact value of $\sin(13 \pi)$ without using a calculator.

Find the exact value of $\cos (-2 \pi)$ without using a calculator.

Find the six trigonometric functions for the angle $\frac{3 \pi}{4}$ . State "not defined" if applicable.

Find the exact values of the six trigonometric functions of $t$ for the point $P=\left(\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right)$ on the unit circle.

Find the value of $\cot \frac{3 \pi}{2} + \cos \frac{3 \pi}{2}$ without a calculator.

Omar needs to find $\cos \left(-\frac{2 \pi}{3}\right)$ . Use the reference angle and quadrant info to solve.

Find the exact value of $\cos \left(-\frac{\pi}{3}\right)$ using reference angles.

Find the values of the trigonometric functions given that $\sin \theta=1$ . What is $\cos \theta$ ? A. $\cos \theta=$ B. Undefined.

Find the six trigonometric functions of $t$ for the point $\left(-\frac{\sqrt{3}}{5},-\frac{\sqrt{22}}{5}\right)$ on the unit circle.

Find the six trigonometric functions for the point $\left(-\frac{1}{\sqrt{26}},-\frac{5}{\sqrt{26}}\right)$ on the unit circle.

Find the six trigonometric functions for the point $\left(-\frac{1}{\sqrt{26}},-\frac{5}{\sqrt{26}}\right)$ on the unit circle.

Find the acute angle $\theta$ where $\sin \theta = \frac{\sqrt{3}}{2}$ . What is $\theta$ in radians?

Find the angle $\alpha$ coterminal with $\theta=\frac{\pi}{14}$ in the range $-2\pi < \alpha < 0$ .

Solve $\cos \left(\frac{x}{2}\right)=-\frac{\sqrt{3}}{2}$ for $x$ in $[0,2\pi)$ . Provide exact radian solutions.

Find the value of $\sin ^{-1}\left[\sin \left(-\frac{7 \pi}{6}\right)\right]$ without a calculator.

Find the family of special angles for $\theta = \frac{14 \pi}{3}$ and its least nonnegative coterminal angle $\theta_{c}$ .

Identify the family of special angles for $-\frac{43 \pi}{6}$ and find the least nonnegative coterminal angle $\theta_{c}$ .

Find the exact value of $\sin \left(-\frac{9 \pi}{2}\right)$ and answer parts a, b, c, and d. Where is the terminal side of $\theta=-\frac{9 \pi}{2}$ ?

Find $\cot(-12\pi)$ exactly. Answer parts a, b, c, and d: a. Where is the terminal side of $\theta = -12\pi$ ?

Find $\cot (-12 \pi)$ without a calculator. a. Where is the terminal side of $\theta=-12 \pi$ ? b. Give the coordinates on the terminal side with $r=1$ .

Find $\cot (-12 \pi)$ by answering: a) Where is $\theta=-12 \pi$ ? b) Coordinates for $r=1$ . c) $\cot \theta$ definition?

Find $\cot(-12\pi)$ : a. Where is $\theta=-12\pi$ ? b. Coordinates on terminal side? c. What is $\cot \theta$ ?

Find the value of $\tan(-7 \pi)$ and answer: a. Where is the terminal side of $\theta=-7 \pi$ ?

Find the reference angle for $\theta=\frac{9 \pi}{4}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

Find the reference angle for $\theta=\frac{29 \pi}{6}$ and the least nonnegative angle coterminal with it. $\theta_{\mathrm{C}}=$

Find the reference angle for $\theta=\frac{29 \pi}{6}$ and the least nonnegative angle coterminal with it. What quadrant is it in?

Find the reference angle for $\theta=\frac{29 \pi}{6}$ and the least nonnegative coterminal angle. What is $\theta_{\mathrm{R}}$ ?

Find the reference angle for $\theta = -\frac{17 \pi}{4}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}} =$

Find the reference angle for $\theta=-\frac{29 \pi}{6}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

Find the reference angle for $\theta=-\frac{29 \pi}{6}$ and the least nonnegative coterminal angle $\theta_{C}$ .

Find the reference angle for $\theta=\frac{48 \pi}{18}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

Find the reference angle for $\theta=\frac{48 \pi}{18}$ and the least nonnegative coterminal angle $\theta_{C}=\frac{2 \pi}{3}$ . In which quadrant is $\theta_{C}$ ?

Find the reference angle for $\theta=\frac{48 \pi}{18}$ and the angle $\theta_{C}=\frac{2 \pi}{3}$ . What is $\theta_{R}$ ?

Find the reference angle for $\theta=\frac{31 \pi}{12}$ . Also, find the least nonnegative angle coterminal with $\theta$ . $\theta_{C}=$

Find the reference angle for $\theta=\frac{31 \pi}{12}$ and the least nonnegative coterminal angle $\theta_{C}$ . What quadrant is $\theta_{C}$ in?

Find the reference angle for $\theta=\frac{31 \pi}{12}$ and the coterminal angle $\theta_{C}=\frac{7 \pi}{12}$ . What is $\theta_{R}$ ?

Find the reference angle for $\theta=-\frac{29 \pi}{12}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

Find the reference angle for $\theta=570^{\circ}$ and the least nonnegative coterminal angle $\theta_{C}$ .

Find the reference angle for $\theta=-\frac{29 \pi}{12}$ and the coterminal angle $\theta_{C}=\frac{19 \pi}{12}$ in quadrant IV. What is $\theta_{R}$ ?

Find the reference angle for $\theta=570^{\circ}$ and the least nonnegative coterminal angle $\theta_{C}$ . What quadrant is $\theta_{C}$ in?

Find the reference angle for $\theta=570^{\circ}$ and the angle $\theta_{C}=210^{\circ}$ in quadrant III. What is $\theta_{R}=\square^{\circ}$ ?

Find the reference angle for $\theta=-420^{\circ}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

Find the reference angle for $\theta=-420^{\circ}$ and the least nonnegative coterminal angle. Which quadrant is $\theta_{C}=300^{\circ}$ in?