$$\sin \theta is $$positive, $$\cos \theta is $$negative

Question 1

Which equation represents the unit circle centered at the origin?

Accepted Answer

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

Question 2

Given the point $$\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$$, is it on the unit circle?

Accepted Answer

Yes, because $$x^2$$ + $$y^2 = 1$

Question 3

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

Accepted Answer

$$30^\circ$$

Question 4

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

Accepted Answer

Quadrant IV

Question 5

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

Accepted Answer

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

Question 6

Which trigonometric function is always positive in Quadrant III?

Accepted Answer

Tangent

Question 7

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

Accepted Answer

$$\sqrt{3}$$

Question 8

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

Accepted Answer

$$180^\circ$$

Question 9

If $$	heta = 120^\circ$$, what is the sign of $$\sin 	heta$$ and $$\cos 	heta$$?

Accepted Answer

$$\sin 	heta is $$positive, $$\cos 	heta is $$negative

Question 10

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

Accepted Answer

ASTC (All Students Take Calculus)

Question 11

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

Accepted Answer

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

Question 12

A medical imaging device rotates $$270^\circ$$ from the positive x-axis. What are the coordinates on the unit circle?

Accepted Answer

$$(0, -1)$$

Question 13

If $$	heta = \frac{5\pi}{6}$$, what is the reference angle?

Accepted Answer

$$\frac{\pi}{6}$$

Question 14

Which of the following points is NOT on the unit circle?

Accepted Answer

$$(2, 0)$$

Question 15

A Ferris wheel rotates through an angle of $$60^\circ. $$What is the sine of this angle?

Accepted Answer

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

Question 16

If $$	heta = 135^\circ$$, what is $$\sin 	heta$$?

Accepted Answer

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

Question 17

Which angle has the same sine, cosine, and tangent values as $$45^\circ$$, except possibly for sign?

Accepted Answer

$$225^\circ$$

Question 18

A clock's minute hand points at $$3 o$$'clock. What is the corresponding angle in radians from the positive x-axis?

Accepted Answer

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

Question 19

If $$	an 	heta is $$undefined, which angle could $$	heta be$$?

Accepted Answer

$$90^\circ$$

Question 20

Which of the following is the correct value for $$\cos 30^\circ$$?

Accepted Answer

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

Unit Circle and Trigonometric Functions: Essential Study Notes for Trigonometry

Study Guide - Practice Questions