$$\theta + 2\pi n$$, 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

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