$$\sin^2$(\theta) + \cos^2$(\theta) = 1$$

Question 1

What is the radian measure of a full circle?

Accepted Answer

$$2\pi$$

Question 2

If an angle measures $$60^\circ$$, what is its radian measure?

Accepted Answer

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

Question 3

On the unit circle, what are the coordinates of the point corresponding to $$\frac{\pi}{2}$$ radians?

Accepted Answer

$$(0, 1)$$

Question 4

What is the value of $$\sin(\frac{\pi}{6})$$?

Accepted Answer

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

Question 5

What is the value of $$\cos(\frac{\pi}{3})$$?

Accepted Answer

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

Question 6

If $$\sin(t) = \frac{1}{4}$$, what are the possible values for $$\cos(t)$$?

Accepted Answer

$$\pm\frac{\sqrt{15}}{4}$$

Question 7

What is the value of $$	an(\frac{\pi}{4})$$?

Accepted Answer

$$1$$

Question 8

Which equation expresses the Pythagorean identity for sine and cosine?

Accepted Answer

$$\sin^2$(	heta) + \cos^2$(	heta) = 1$$

Question 9

A kite string is 450 ft long and makes a $$30^\circ$$ angle with the ground. How high is the kite above the ground?

Accepted Answer

$$450 \cdot \sin(30^\circ) = 225 ft$$

Question 10

What is the value of $$\sin(2\pi + \frac{\pi}{6})$$?

Accepted Answer

$$\sin(\frac{\pi}{6})$$

Question 11

What is the value of $$\cos(7\pi/4)$$?

Accepted Answer

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

Question 12

If $$\sin(3\pi/8) = 0.924$$, what is $$\cos(3\pi/8)$$?

Accepted Answer

$$\sqrt{1 - (0.924)^2$}$$

Question 13

What is the value of $$	an(3\pi/4)$$?

Accepted Answer

$$-1$$

Question 14

Which of the following is true about $$\sin(-t)$$?

Accepted Answer

$$-\sin(t)$$

Question 15

What is the value of $$\sin(14\pi/3)$$?

Accepted Answer

$$\sin(2\pi + 2\pi + \frac{2\pi}{3}) = \sin(\frac{2\pi}{3})$$

Question 16

If $$\cos(	heta) = -\frac{1}{2}$$, which quadrant(s) could $$	heta be in$$?

Accepted Answer

Quadrant II or III

Question 17

What is the value of $$\sin(5\pi/6)$$?

Accepted Answer

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

Question 18

What is the value of $$\cos(5\pi/3)$$?

Accepted Answer

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

Question 19

If $$\sin^2$(x) + \cos^2$(x) = 1$$, what is $$\cos^2$(x) if$$ $$\sin(x) = 0.6$$?

Accepted Answer

$$1 - (0.6)^2$ = 0.64$$

Unit Circle, Radian Measure, and Trigonometric Functions: Study Guide

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