Question 1

Which of the following equations represents the unit circle in the coordinate plane?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 2

If a point $$(a, b)$$ lies on the unit circle, which of the following points also lies on the unit circle due to symmetry?

Accepted Answer

All of the above

Question 3

Given $$\cos s = x$$ and $$\sin s = y$$ for a point $$(x, y) on $$the unit circle, which identity is always true?

Accepted Answer

$$\cos^2$ s + \sin^2$ s = 1$$

Question 4

What is the exact value of $$\cos \frac{2\pi}{3}$$?

Accepted Answer

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

Question 5

Which of the following is the correct domain for the sine and cosine circular functions?

Accepted Answer

$$(-\infty, \infty)$$

Question 6

A calculator is used to find $$\cos(1.85). $$Which mode should the calculator be in?

Accepted Answer

Radian mode

Question 7

If $$	an s = 1$$ and $$s is in$$ $$[\pi, \frac{3\pi}{2}]$$, what is the exact value of $$s$$?

Accepted Answer

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

Question 8

Which of the following best describes the reference arc for a point on the unit circle?

Accepted Answer

The shortest arc from the point to the nearest point on the x-axis

Question 9

Given $$\sin 	heta = y$$ and $$\cos 	heta = x$$ for a point $$(x, y) on $$the unit circle, what is $$	an 	heta in $$terms of $$x$$ and $$y$$?

Accepted Answer

$$\frac{y}{x}$$

Question 10

Suppose the angle of elevation $$	heta of $$the sun is modeled by $$\sin 	heta = \cos D \cos L \cos \omega + \sin D \sin L. If$$ $$D = -0.1425$$, $$L = 0.6720$$, and $$\omega = 0.7854$$, what is the approximate value of $$	heta in $$radians?

Accepted Answer

$$0.4773$$

Question 11

Which of the following is the correct value for $$	an\left(-\frac{5\pi}{3}ight)$$?

Accepted Answer

$$\sqrt{3}$$

Question 12

If $$\cos s = 0.9685$$ and $$s \in [0, \frac{\pi}{2}]$$, what is the approximate value of $$s$$?

Accepted Answer

$$0.2517$$

Question 13

Which of the following points on the unit circle corresponds to $$	heta = \frac{\pi}{3}$$?

Accepted Answer

$$\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$$

Question 14

What is the value of $$\sin \frac{3\pi}{2}$$?

Accepted Answer

$$-1$$

Question 15

Which of the following is the correct value for $$\cos \frac{7\pi}{4}$$?

Accepted Answer

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

Question 16

If $$\sin 	heta = y$$ and $$\cos 	heta = x$$ for a point $$(x, y) on $$the unit circle, what is the value of $$\csc 	heta$$?

Accepted Answer

$$\frac{1}{y}$$

Question 17

Which of the following is a common error when evaluating circular functions with a calculator?

Accepted Answer

Using degree mode instead of radian mode

Question 18

If $$\cos 	heta = x$$ and $$\sin 	heta = y$$ for a point $$(x, y) on $$the unit circle, which of the following is the correct value for $$\sec 	heta$$?

Accepted Answer

$$\frac{1}{x}$$

Question 19

Suppose you are given the point $$\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right) on $$the unit circle. What is the corresponding angle in radians in $$[0, 2\pi)$$?

Accepted Answer

$$\frac{2\pi}{3}$$

Radian Measure and the Unit Circle: Circular Functions and Their Applications

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