Question 1

Which equation represents the unit circle in the coordinate plane?

Accepted Answer

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

Question 2

If $$s is a $$real number and $$(x, y) is $$the point on the unit circle corresponding to $$s$$, which of the following is always true?

Accepted Answer

$$x = 	ext{cos} s$$

Question 3

What is the domain of the sine and cosine functions?

Accepted Answer

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

Question 4

Which trigonometric function is undefined at $$s = \pi$$?

Accepted Answer

$$\csc s$$

Question 5

If $$s = \frac{\pi}{2}$$, what are the coordinates of the corresponding point on the unit circle?

Accepted Answer

$$(0, 1)$$

Question 6

Which identity is true for all $$s$$ where $$\cos s 
eq 0$$?

Accepted Answer

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

Question 7

If $$s = 3$$ and the corresponding point $$(x, y) on $$the unit circle is in quadrant II, which of the following is true?

Accepted Answer

$$x  0$$

Question 8

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

Accepted Answer

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

Question 9

Which trigonometric function is undefined for $$s = n\pi$$, where $$n is $$any integer?

Accepted Answer

$$\cot s$$

Question 10

If $$\cos s = 0$$ and $$\sin s = -1$$, what is the value of $$s$$?

Accepted Answer

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

Question 11

Which quadrant contains the point on the unit circle corresponding to $$s if$$ $$\cos s \u003c 0$$ and $$\sin s \u003c 0$$?

Accepted Answer

Quadrant III

Question 12

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

Accepted Answer

$$-1$$

Question 13

If $$s = \frac{\pi}{4}$$, what is the value of $$	an s$$?

Accepted Answer

$$1$$

Question 14

Which of the following statements about the unit circle is correct?

Accepted Answer

The radius is always $$1$$ unit.

Question 15

If $$s = \frac{\pi}{3}$$, what is the value of $$\cos s$$?

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 16

Which trigonometric function is positive in quadrant IV?

Accepted Answer

$$\cos s$$

Question 17

If $$s = 4.5$$ radians, which quadrant does the corresponding point on the unit circle lie in?

Accepted Answer

Quadrant III

Question 18

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

Accepted Answer

$$1$$

Question 19

Which of the following is a true statement about the periodicity of sine and cosine functions?

Accepted Answer

$$\sin(s + 2n\pi) = \sin s$$ for any integer $$n$$

The Unit Circle and the Functions of Trigonometry

Study Guide - Practice Questions