$$\tan x = \frac{\sin x}{\cos x}$$

Question 1

Which of the following is the correct value for $$\sin\left(\frac{\pi}{4}\right)$$?

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 2

Given $$\sin	heta = \frac{2}{3}$$ and $$	heta is in $$Quadrant II, what is the value of $$\cos	heta$$?

Accepted Answer

$$-\frac{\sqrt{5}}{3}$$

Question 3

Which of the following is a Pythagorean identity?

Accepted Answer

$$	an^2$x + 1 = \sec^2$x$$

Question 4

What is the reference angle for $$210^\circ$$?

Accepted Answer

$$30^\circ$$

Question 5

If $$\cos$$^{-1}$$\left(-\frac{\sqrt{3}}{2}\right) is $$evaluated, which angle in radians is the result?

Accepted Answer

$$\frac{4\pi}{3}$$

Question 6

Which of the following is the correct sum formula for $$\sin(a + b)$$?

Accepted Answer

$$\sin a \cos b + \cos a \sin b$$

Question 7

A truck's wheels spin at 200 rotations per minute with a radius of 13 inches. What is the speed of the truck in miles per hour? (1 mile = 5280 ft)

Accepted Answer

$$\approx 31$$ mph

Question 8

A support cable is attached to a utility pole at a height of 10 ft and forms a $$50^\circ$$ angle with the ground. How long is the cable?

Accepted Answer

$$\frac{10}{\sin 50^\circ}$$

Question 9

If $$	an	heta = 2$$ and $$	heta is in $$Quadrant III, what is the exact value of $$\cos	heta$$?

Accepted Answer

$$-\frac{1}{\sqrt{5}}$$

Question 10

What is the exact value of $$\sin 345^\circ$$ using sum or difference identities?

Accepted Answer

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

Question 11

Solve for $$x in$$ $$\sin x = -\frac{1}{2}$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \frac{7\pi}{6}, \frac{11\pi}{6}$$

Question 12

Which of the following is the correct double-angle identity for $$\cos 2x$$?

Accepted Answer

$$2\cos^2$x - 1$$

Question 13

If $$	heta is in $$Quadrant II and $$\sin	heta = \frac{2}{3}$$, what is $$	an	heta$$?

Accepted Answer

$$-\frac{2}{\sqrt{5}}$$

Question 14

What is the value of $$\cos\left(\sin$$^{-1}$$\left(-\frac{3}{4}\right)\right)$$?

Accepted Answer

$$\frac{\sqrt{7}}{4}$$

Question 15

Solve the triangle: $$A = 35^\circ$$, $$a = 8$$, $$b = 11. $$What is the value of angle $$B$$?

Accepted Answer

$$B \approx 54^\circ$$

Question 16

Which of the following is the correct reciprocal identity?

Accepted Answer

$$\csc x = \frac{1}{\sin x}$$

Question 17

If $$\cos 3x = -\frac{\sqrt{3}}{2}$$, what is one solution for $$x in$$ $$0 \leq x \u003c 2\pi$$?

Accepted Answer

$$x = \frac{5\pi}{18}$$

Question 18

Which of the following is the correct quotient identity?

Accepted Answer

$$	an x = \frac{\sin x}{\cos x}$$

Question 19

A triangle has $$B = 62^\circ$$, $$a = 10$$, $$c = 12. $$Using the Law of Sines, what is the formula for finding angle $$C$$?

Accepted Answer

$$\sin C = \frac{a \sin B}{c}$$

Trigonometry Final Exam Review – Step-by-Step Guidance

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