Question 1

A right triangle has legs $$a = 2$$ and $$b = 3. $$What is the exact value of $$\sin(A)$$, where $$A is $$the angle opposite side $$a$$? Express your answer with a rational denominator.

Accepted Answer

$$\frac{2}{\sqrt{13}}$$

Question 2

Convert $$75.25^\circ to $$radians. Round your answer to two decimal places.

Accepted Answer

$$1.31$$ radians

Question 3

Convert $$123.456^\circ to $$degrees, minutes, and seconds. Round your answer to the nearest second.

Accepted Answer

$$123^\circ 27' 21''$$

Question 4

Convert $$60^\circ to $$radians. Express your answer in terms of $$\pi.$$

Accepted Answer

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

Question 5

Convert $$\frac{5\pi}{6}$$ radians to degrees.

Accepted Answer

$$150^\circ$$

Question 6

Given $$\sin(	heta) = \frac{3}{5}$$ and $$\cos(	heta) = \frac{4}{5}$$, find $$	an(	heta).$$

Accepted Answer

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

Question 7

Use fundamental identities to find the exact value of $$\sin(90^\circ - x) if$$ $$\cos(x) = \frac{1}{2}.$$

Accepted Answer

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

Question 8

If $$	heta = 45^\circ$$, find the exact value of $$\sin(2	heta).$$

Accepted Answer

$$1$$

Question 9

The point $$(3, 4) is on $$the terminal side of angle $$	heta. $$What is $$\sin(	heta)$$?

Accepted Answer

$$\frac{4}{5}$$

Question 10

A 25-foot ladder leans against a house, forming a $$60^\circ$$ angle with the ground. How tall is the house? Round your answer to the nearest 0.1 foot.

Accepted Answer

$$21.7$$ feet

Question 11

In which quadrant does the angle $$	heta$$ lie if $$\sin(	heta)  0$$?

Accepted Answer

Quadrant IV

Question 12

Determine the sign of $$\sin(-120^\circ).$$

Accepted Answer

Negative

Question 13

Find the reference angle for $$-135^\circ.$$

Accepted Answer

$$45^\circ$$

Question 14

Use the reference angle to find the exact value of $$\sin(-150^\circ).$$

Accepted Answer

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

Question 15

Find the exact value of $$	an(	heta)$$ given that $$\sin(	heta) = \frac{5}{13}$$ and $$\cos(	heta) \u003c 0.$$

Accepted Answer

$$-\frac{5}{12}$$

Question 16

If $$\sin(	heta) = -\frac{3}{5}$$, find $$\sin(	heta + \pi).$$

Accepted Answer

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

Question 17

Use the even-odd properties to find the exact value of $$\cos(-x).$$

Accepted Answer

$$\cos(x)$$

Question 18

Find the exact value of $$\sin(\pi - x).$$

Accepted Answer

$$-\sin(x)$$

Question 19

A sound wave is modeled by $$y = 3\sin(2x - \frac{\pi}{4}). $$What are the amplitude, period, and phase shift?

Accepted Answer

Amplitude: $$3$$, Period: $$\pi$$, Phase shift: $$\frac{\pi}{8} to $$the right

Question 20

A Ferris wheel rotates such that its height above the ground is modeled by $$h(t) = 10\cos(\frac{\pi}{6}t) + 20. $$What is the amplitude, period, and midline of the function?

Accepted Answer

Amplitude: $$10$$, Period: $$12$$, Midline: $$20$$

Trigonometry Review 1 – Step-by-Step Guidance

Study Guide - Practice Questions

Study Guide - Flashcards