Q: Find the exact value of $$\\cos 165^\\circ$$ using sum and difference identities.

$$-\\frac{\\sqrt{6} + \\sqrt{2}}{4}$$

Q: Rewrite $$\\sin 19^\\circ \\sin 21^\\circ as a $$sum or difference of trigonometric functions.

$$\\frac{1}{2}[\\cos(19^\\circ - 21^\\circ) - \\cos(19^\\circ + 21^\\circ)]$$

Q: Find the exact value of $$\\sin \\frac{5\\pi}{12}$$ using a half-angle identity.

$$\\frac{\\sqrt{6} - \\sqrt{2}}{4}$$

Q: Find the value of $$s in $$the interval $$[\\frac{\\pi}{2}, \\pi]$$ such that $$\\sin s = -1.$$

No solution in $$[\\frac{\\pi}{2}, \\pi]$$

Question 1

Convert $$330^\circ to $$radians. Leave your answer in terms of $$\pi.$$

Accepted Answer

$$\frac{11\pi}{6}$$

Question 2

Convert $$-\frac{7\pi}{4}$$ radians to degrees.

Accepted Answer

$$-315^\circ$$

Question 3

Evaluate $$\sin \frac{5\pi}{6}.$$

Accepted Answer

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

Question 4

A pulley has a radius of $$14.0 cm. It $$takes $$15$$ seconds for $$40 cm of $$belt to go around the pulley. Find the angular velocity of the pulley in radians per second.

Accepted Answer

$$0.18$$ radians/sec

Question 5

Find the length of an arc intercepted by a central angle of $$210^\circ in a $$circle of radius $$15.6 in.$$

Accepted Answer

$$55.3 in.$$

Question 6

Given $$\cos \theta = -\frac{12}{13}$$ and $$\sin \theta = \frac{5}{13}$$ with $$\theta in $$quadrant II, find $$\sin(2\theta).$$

Accepted Answer

$$-\frac{120}{169}$$

Question 7

Find the exact value of $$\tan 170^\circ - \tan 50^\circ.$$

Accepted Answer

$$-1$$

Question 8

Use the double-angle identity to write $$1 - 2\sin^2$ x as a $$single trigonometric function.

Accepted Answer

$$\cos 2x$$

Question 9

Find the exact value of $$\cos 165^\circ$$ using sum and difference identities.

Accepted Answer

$$-\frac{\sqrt{6} + \sqrt{2}}{4}$$

Question 10

Given $$\sin \theta = \frac{8}{17}$$ and $$\theta is in $$quadrant II, find $$\tan \theta.$$

Accepted Answer

$$-\frac{8}{15}$$

Question 11

Rewrite $$\sin 19^\circ \sin 21^\circ as a $$sum or difference of trigonometric functions.

Accepted Answer

$$\frac{1}{2}[\cos(19^\circ - 21^\circ) - \cos(19^\circ + 21^\circ)]$$

Question 12

Find the exact value of $$\sin \frac{5\pi}{12}$$ using a half-angle identity.

Accepted Answer

$$\frac{\sqrt{6} - \sqrt{2}}{4}$$

Question 13

A point on the edge of a drum rotates $$52$$ times per minute. The diameter of the drum is $$16.0 in. $$Find the linear velocity in inches per minute.

Accepted Answer

$$832.2$$ inches/min

Question 14

Evaluate $$\tan \frac{3\pi}{4}.$$

Accepted Answer

$$-1$$

Question 15

Find the exact value of $$\cos \frac{7\pi}{6}.$$

Accepted Answer

$$-\frac{\sqrt{3}}{2}$$

Question 16

Find the approximate value of $$\sin 52^\circ to $$four decimal places.

Accepted Answer

$$0.7880$$

Question 17

If $$\cos s = -\frac{5}{13}$$ and $$s is in $$quadrant II, find $$\sin s.$$

Accepted Answer

$$\frac{12}{13}$$

Question 18

Find the value of $$s in $$the interval $$[\frac{\pi}{2}, \pi]$$ such that $$\sin s = -1.$$

Accepted Answer

No solution in $$[\frac{\pi}{2}, \pi]$$

Question 19

Use the fundamental identities to find $$\sin t if$$ $$\sin t = \frac{8}{17}$$ and $$t is in $$quadrant II.

Accepted Answer

$$\frac{8}{17}$$

Comprehensive Study Guide: Core Topics in College Trigonometry

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