$\theta + 2\pi n$, where $n$ is any integer

Question 1

Given the angle $\frac{23\pi}{5}$, which of the following is its coterminal angle between $0$ and $2\pi$?

Accepted Answer

$\frac{13\pi}{5}$

Question 2

If an angle measures $-15\pi$, what is its coterminal angle between $0$ and $2\pi$?

Accepted Answer

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

Question 3

Which of the following best describes coterminal angles?

Accepted Answer

Angles that differ by a multiple of $2\pi$ and share the same terminal side

Question 4

A Ferris wheel rotates through an angle of $\frac{23\pi}{5}$ radians. How many full rotations has it completed?

Accepted Answer

2 full rotations plus $\frac{3\pi}{5}$ radians

Question 5

Which equation can be used to find a positive coterminal angle for $-15\pi$?

Accepted Answer

$-15\pi + 2\pi n$, where $n$ is a positive integer

Question 6

If $	heta = \frac{23\pi}{5}$, which of the following is NOT a coterminal angle?

Accepted Answer

$\frac{23\pi}{5} 	imes 2$

Question 7

A clock’s minute hand moves through $\frac{10\pi}{5}$ radians. What is the equivalent angle in degrees?

Accepted Answer

$180^\circ$

Question 8

Which of the following is the correct way to convert $\frac{23\pi}{5}$ to a positive angle less than $2\pi$?

Accepted Answer

Subtract $2\pi$ until the result is less than $2\pi$

Question 9

If an angle is negative and less than one full rotation, what must you do to find its coterminal angle between $0$ and $2\pi$?

Accepted Answer

Add $2\pi$ to the angle

Question 10

Which of the following statements is true about coterminal angles?

Accepted Answer

Coterminal angles can be positive or negative

Question 11

A rotating platform completes $-15\pi$ radians. How many full rotations is this equivalent to?

Accepted Answer

-7.5 rotations

Question 12

Which of the following angles is coterminal with $\frac{23\pi}{5}$?

Accepted Answer

$\frac{13\pi}{5}$

Question 13

If you rotate a ray by $\frac{23\pi}{5}$ radians, which of the following is true?

Accepted Answer

The ray ends at the same position as a rotation of $\frac{13\pi}{5}$ radians

Question 14

Which formula gives all coterminal angles for a given angle $	heta$?

Accepted Answer

$	heta + 2\pi n$, where $n$ is any integer

Question 15

A wheel turns through $\frac{23\pi}{5}$ radians. What is the smallest positive coterminal angle?

Accepted Answer

$\frac{13\pi}{5}$

Angles, Coterminal Angles, and Rotations in Precalculus

Study Guide - Practice Questions