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

Study Guide - Practice Questions