Question 1

Which of the following angles is NOT a member of the Quadrantal Family of Angles?

Accepted Answer

$$\frac{5\pi}{6}$$

Question 2

If the terminal side of an angle $$	heta$$ lies in Quadrant III, which trigonometric functions are positive?

Accepted Answer

Tangent and cotangent

Question 3

Given a point $$P(x, y) on $$the terminal side of an angle $$	heta in $$standard position, what is the general definition of $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \frac{y}{x}$$

Question 4

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

Accepted Answer

$$30^\circ$$

Question 5

If $$	heta = \frac{5\pi}{6}$$, in which quadrant does its terminal side lie and what is the sign of $$\sin 	heta$$?

Accepted Answer

Quadrant II, positive

Question 6

A point $$P(-3, 4)$$ lies on the terminal side of an angle $$	heta in $$standard position. What is $$\sin 	heta$$?

Accepted Answer

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

Question 7

Which of the following is the correct value for $$	an 	heta$$ when $$	heta = \frac{3\pi}{2}$$?

Accepted Answer

Undefined

Question 8

If the terminal side of an angle $$	heta$$ lies in Quadrant IV, which trigonometric functions are positive?

Accepted Answer

Cosine and secant

Question 9

What is the value of $$\sec 	heta$$ when $$	heta = \pi$$?

Accepted Answer

$$-1$$

Question 10

A pilot is flying at an angle of $$135^\circ$$ from the positive x-axis. What is the reference angle?

Accepted Answer

$$45^\circ$$

Question 11

If $$	heta = \frac{7\pi}{6}$$, what is the reference angle and in which quadrant does the terminal side lie?

Accepted Answer

Reference angle $$= \frac{\pi}{6}$$, Quadrant III

Question 12

Which of the following is the correct formula for the distance $$r$$ from the origin to a point $$P(x, y)$$?

Accepted Answer

$$r = \sqrt{x^2$ + y^2$}$$

Question 13

If $$	heta = 300^\circ$$, what is the reference angle?

Accepted Answer

$$60^\circ$$

Question 14

Which of the following angles is coterminal with $$\frac{2\pi}{3}$$?

Accepted Answer

$$\frac{8\pi}{3}$$

Question 15

A medical imaging device rotates $$225^\circ$$ from the positive x-axis. In which quadrant does the terminal side lie and what is the reference angle?

Accepted Answer

Quadrant III, $$45^\circ$$

Question 16

If $$	heta = \frac{3\pi}{4}$$, what is the value of $$\sin 	heta$$?

Accepted Answer

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

Question 17

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

Accepted Answer

Sine and cosecant are positive

Question 18

If $$	heta = \frac{5\pi}{3}$$, what is the reference angle?

Accepted Answer

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

Question 19

A surveyor measures an angle of $$120^\circ$$ from the positive x-axis. What is the sign of $$\cos 120^\circ$$?

Accepted Answer

Negative

Question 20

Which of the following is the correct definition of $$\csc 	heta in $$terms of $$x$$, $$y$$, and $$r$$?

Accepted Answer

$$\csc 	heta = \frac{r}{y}$$

Special Angle Families and Trigonometric Functions in the Coordinate Plane

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