Question 1

Which of the following best describes a reference angle?

Accepted Answer

The angle formed by the terminal side of a given angle and the x-axis, always measured as a positive value less than or equal to $$90^{\circ}.$$

Question 2

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

Accepted Answer

$$30^{\circ}$$

Question 3

If $$	heta = 135$$^{\circ}$$, what is its reference angle?

Accepted Answer

$$45^{\circ}$$

Question 4

Which quadrant does the angle $$240^{\circ}$$ lie in, and what is the sign of $$\sin(240$$^{\circ}$$)$$?

Accepted Answer

Quadrant III, positive

Question 5

Given $$	an(745$$^{\circ}$$)$$, what is the coterminal angle between $$0^{\circ}$$ and $$360^{\circ}$$?

Accepted Answer

$$25^{\circ}$$

Question 6

Which of the following is the reference angle for $$5\pi/6$$ radians?

Accepted Answer

$$\pi/6$$

Question 7

If $$\sin(	heta) = -\dfrac{\sqrt{3}}{2}$$ and $$	heta is $$between $$180^{\circ}$$ and $$360^{\circ}$$, what could $$	heta be$$?

Accepted Answer

$$240^{\circ}$$

Question 8

What is the exact value of $$\cos(330$$^{\circ}$$)$$?

Accepted Answer

$$\dfrac{\sqrt{3}}{2}$$

Question 9

Which of the following angles has the same sine value as $$150^{\circ}$$?

Accepted Answer

$$30^{\circ}$$

Question 10

If $$	heta = 7\pi/4$$, what is its reference angle?

Accepted Answer

$$\pi/4$$

Question 11

A medical imaging device rotates $$520^{\circ}$$ from its starting position. What is its coterminal angle?

Accepted Answer

$$160^{\circ}$$

Question 12

Which quadrant does the angle $$5\pi/3$$ lie in, and what is the sign of $$	an(5\pi/3)$$?

Accepted Answer

Quadrant IV, negative

Question 13

If $$\cos(	heta) = -\dfrac{1}{2}$$ and $$	heta is in $$Quadrant II, what is $$	heta$$?

Accepted Answer

$$120^{\circ}$$

Question 14

What is the reference angle for $$340^{\circ}$$?

Accepted Answer

$$20^{\circ}$$

Question 15

Which of the following is a coterminal angle of $$-45^{\circ}$$?

Accepted Answer

$$315^{\circ}$$

Question 16

If $$	an(	heta) = 1$$ and $$	heta is in $$Quadrant III, what is $$	heta$$?

Accepted Answer

$$225^{\circ}$$

Question 17

A Ferris wheel rotates $$13\pi/3$$ radians from its starting position. What is its coterminal angle in radians?

Accepted Answer

$$\pi/3$$

Question 18

Which of the following is the reference angle for $$11\pi/6$$?

Accepted Answer

$$\pi/6$$

Question 19

If $$\sin(	heta) = -\dfrac{1}{2}$$ and $$	heta is in $$Quadrant IV, what is $$	heta$$?

Accepted Answer

$$330^{\circ}$$

Question 20

Which of the following angles has the same cosine value as $$300^{\circ}$$?

Accepted Answer

$$60^{\circ}$$

Reference Angles and Trigonometric Values on the Unit Circle

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