Question 1

Which of the following points is ON the unit circle defined by $$x^2$$ + $$y^2 = 1$?

Accepted Answer

$$(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$$

Question 2

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

Accepted Answer

$$30^\circ$$

Question 3

In which quadrant does the angle $$\frac{7\pi}{4}$$ radians lie?

Accepted Answer

Quadrant IV

Question 4

If $$\sin 	heta = \frac{1}{2}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

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

Question 5

Which trigonometric function is ALWAYS positive in Quadrant III?

Accepted Answer

Tangent

Question 6

Find $$	an 60^\circ$$ using the unit circle.

Accepted Answer

$$\sqrt{3}$$

Question 7

A point $$\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right) is $$given. Is this point on the unit circle?

Accepted Answer

Yes, because $$\left(-\frac{\sqrt{2}}{2}\$$right)^2$$ + \left(-\frac{\sqrt{2}}{2}\$$right)^2$$ = 1$$

Question 8

What is the value of $$\sin 45^\circ$$?

Accepted Answer

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

Question 9

If $$	heta = 120^\circ$$, what is its reference angle?

Accepted Answer

$$60^\circ$$

Question 10

Which of the following is the correct equation for the unit circle centered at the origin?

Accepted Answer

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

Question 11

A medical imaging device rotates $$270^\circ$$ from its starting position. In which quadrant does its beam point?

Accepted Answer

Quadrant IV

Question 12

If $$\cos 	heta = 0$$ and $$	heta is $$between $$0^\circ$$ and $$360^\circ$$, what are the possible values of $$	heta$$?

Accepted Answer

$$90^\circ$$ and $$270^\circ$$

Question 13

Which mnemonic helps remember which trig functions are positive in each quadrant?

Accepted Answer

ASTC (All Students Take Calculus)

Question 14

A Ferris wheel rotates through an angle of $$\frac{5\pi}{6}$$ radians. In which quadrant is the passenger located?

Accepted Answer

Quadrant II

Question 15

What is the value of $$\cos 30^\circ$$?

Accepted Answer

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

Question 16

If $$	an 	heta is $$undefined, which of the following could be the value of $$	heta$$?

Accepted Answer

$$90^\circ$$

Question 17

A clock's minute hand points at $$135^\circ. $$What is the reference angle?

Accepted Answer

$$45^\circ$$

Question 18

Which of the following is TRUE about the signs of trigonometric functions in Quadrant II?

Accepted Answer

Sine is positive, cosine and tangent are negative

Question 19

If $$\sin 	heta = -\frac{1}{2}$$ and $$	heta is $$between $$180^\circ$$ and $$360^\circ$$, which quadrant is $$	heta in$$?

Accepted Answer

Quadrant III or IV

Question 20

A satellite moves to the position $$(-1, 0) on $$the unit circle. What is the corresponding angle in degrees?

Accepted Answer

$$180^\circ$$

The Unit Circle and Trigonometric Functions: A Precalculus Study Guide

Study Guide - Practice Questions