Q: Given $$\cot \theta = -\frac{4}{5}$$ and $$\theta is in $$quadrant IV, find $$\sin \theta.$$

$$\sin \theta = \frac{5}{\sqrt{41}}$$

Q: If $$\tan \theta = -\frac{10}{3}$$ and $$\cos \theta \u003e 0$$, what is $$\sin \theta$$?

$$\sin \theta = -\frac{10}{\sqrt{109}}$$

Q: Given $$\cot \theta = \frac{5}{12}$$ and $$\sin \theta \u003c 0$$, find $$\sin \theta.$$

$$\sin \theta = -\frac{5}{13}$$

Question 1

Given $$\cot 	heta = -\frac{4}{5}$$ and $$	heta is in $$quadrant IV, find $$\sin 	heta.$$

Accepted Answer

$$\sin 	heta = \frac{5}{\sqrt{41}}$$

Question 2

If $$	an 	heta = -\frac{10}{3}$$ and $$\cos 	heta \u003e 0$$, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = -\frac{10}{\sqrt{109}}$$

Question 3

Which trigonometric function is graphed if the graph is symmetric about the y-axis, and is it even or odd?

Accepted Answer

The function is $$\sec x$$, which is even.

Question 4

Given $$\cot 	heta = \frac{5}{12}$$ and $$\sin 	heta \u003c 0$$, find $$\sin 	heta.$$

Accepted Answer

$$\sin 	heta = -\frac{5}{13}$$

Question 5

Simplify $$\sec x - \frac{1}{\sec x} so $$that there are no quotients in the final expression.

Accepted Answer

$$\frac{1}{\cos x} - \cos x$$

Question 6

Write $$\sin \beta 	an \beta / \cos \beta as a $$single trigonometric function or power.

Accepted Answer

$$	an \beta$$

Question 7

Verify the identity: $$\csc x \cot x = \sec x. $$Which transformation should be applied first?

Accepted Answer

Apply a reciprocal identity.

Question 8

Find the exact value of $$\cos(-105^\circ).$$

Accepted Answer

$$\cos(-105^\circ) = -\frac{\sqrt{2} + \sqrt{6}}{4}$$

Question 9

Given $$\sin s = -\frac{2}{5}$$ and $$\sin t = -\frac{7}{8}$$, both in quadrant III, find $$\cos(s+t).$$

Accepted Answer

$$\cos(s+t) = -\frac{56}{65}$$

Question 10

Use a double-angle identity to find $$\cos 30^\circ - \sin 30^\circ.$$

Accepted Answer

$$\cos 30^\circ - \sin 30^\circ = \frac{\sqrt{3} - 1}{2}$$

Question 11

Find the exact value of $$	an$$^{-1}$$(-\frac{1}{\sqrt{3}}).$$

Accepted Answer

$$-\frac{\pi}{6}$$

Question 12

Solve for $$x in$$ $$3 \cot x + 2 = -1$$ over $$[0, 2\pi).$$

Accepted Answer

$$x = \frac{3\pi}{4}, \frac{7\pi}{4}$$

Question 13

A surveyor measures $$BC = 365 m$$, angle $$B = 114^\circ 30'$$ and angle $$C = 12^\circ 10'. $$Find the distance $$AB$$ across the river.

Accepted Answer

$$AB = 96 m$$

Question 14

A ship starts at a bearing of $$N20^\circ E$$ and after sailing $$8.2$$ miles due south, its new bearing is $$N30^\circ E. $$What was the initial distance from the lighthouse?

Accepted Answer

$$25$$ miles

Question 15

Find the area of triangle $$ABC$$ with $$a = 12.23 in$$, $$b = 5.91 in$$, and $$C = 13.39^\circ.$$

Accepted Answer

$$8.4$$\ 	ext{in}^2$

Question 16

Given $$a = 4.02 m$$, $$c = 5.68 m$$, and $$B = 28.5^\circ$$, find the length of side $$b.$$

Accepted Answer

$$b = 2.8792$$\ 	ext{m}$

Question 17

A weight is supported by cables attached to both ends of a horizontal beam. The cables are $$35 ft $$and $$65 ft $$long, and the distance between their attachment points is $$95 ft. $$What is the angle between the beam and the $$35 ft $$cable?

Accepted Answer

$$38^\circ$$

Question 18

Use an appropriate area formula to find the area of a triangle with sides $$a = 15 m$$, $$b = 9 m$$, $$c = 12 m.$$

Accepted Answer

$$54.0$$\ 	ext{m}^2$

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