Quiz: Coterminal and Reference Angles

Authored by David Granda

Mathematics

9th - 12th Grade

CCSS covered

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24 questions

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MULTIPLE CHOICE QUESTION

2 mins • 5 pts

Find the reference angle.

$-\frac{4\pi}{9}$

$\frac{2\pi}{9}$

$-\frac{5\pi}{18}$

$\frac{5\pi}{18}$

Answer explanation

$\pi-\frac{13\pi}{18}=\frac{18\pi}{18}-\frac{13\pi}{18}=\frac{5\pi}{18}$ Treat it as if in quadrant II.

MULTIPLE CHOICE QUESTION

2 mins • 5 pts

Find the reference angle.

$-\frac{\pi}{4}$

$\frac{\pi}{4}$

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

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

Answer explanation

$\frac{5\pi}{4}-\pi=\frac{5\pi}{4}-\frac{4\pi}{4}=\frac{\pi}{4}$
The angle is in quadrant III

MULTIPLE CHOICE QUESTION

2 mins • 5 pts

What is the reference angle for $\frac{2\pi}{3}$

$\frac{\pi}{4}$

$\frac{7\pi}{6}$

$\frac{4\pi}{3}$

$\frac{\pi}{3}$

Answer explanation

The angle is in quadrant II, subtract it from $\pi$
$\pi-\frac{2\pi}{3}=\frac{3\pi}{3}-\frac{2\pi}{3}=\frac{\pi}{3}$

MULTIPLE CHOICE QUESTION

2 mins • 5 pts

Which angle is COTERMINAL to $\frac{\pi}{4}$ ?

$\frac{7\pi}{4}$

$\frac{3\pi}{4}$

$-\frac{5\pi}{4}$

$\frac{9\pi}{4}$

Answer explanation

Add or subtract $2\pi$ to the angle

MULTIPLE SELECT QUESTION

2 mins • 5 pts

Which of the following angles are coterminal to the angle $-\frac{5\pi}{3}$ ? Select all that apply.

$\frac{\pi}{3}$

$-\frac{11\pi}{3}$

$\frac{7\pi}{3}$

$-\frac{15\pi}{3}$

Answer explanation

Add or subtract $2\pi$ to the angle

MULTIPLE SELECT QUESTION

2 mins • 5 pts

Which of the following angles are coterminal to the angle $-\frac{3\pi}{4}$ ? Select all that apply.

$\frac{7\pi}{4}$

$\frac{\pi}{4}$

$-\frac{7\pi}{4}$

$-\frac{11\pi}{4}$

Answer explanation

Add or subtract $2\pi$ to the angle

MULTIPLE CHOICE QUESTION

2 mins • 5 pts

Are $-\frac{3\pi}{4}$ and $\frac{5\pi}{4}$ coterminal angles?

Yes

Answer explanation

Add or subtract $2\pi$ to the angle and it should give you the other.

MULTIPLE CHOICE QUESTION

2 mins • 5 pts

Are $\frac{15\pi}{4}$ and $-\frac{3\pi}{4}$ coterminal angles?

Yes

MULTIPLE CHOICE QUESTION

2 mins • 5 pts

To find an angle that is coterminal to a given angle, add or subtract _______________ and the given angle.

$\pi$

$\frac{\pi}{2}$

$3\pi$

$2\pi$

10.

MULTIPLE CHOICE QUESTION

2 mins • 5 pts

What is the reference angle for 125°?

235°

125°

75°

55°

Answer explanation

$180\degree-125\degree=55\degree$
The angle is in quadrant II

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Quiz: Coterminal and Reference Angles

Find the reference angle.

π−13π18=18π18−13π18=5π18\pi-\frac{13\pi}{18}=\frac{18\pi}{18}-\frac{13\pi}{18}=\frac{5\pi}{18}π−1813π​=1818π​−1813π​=185π​ Treat it as if in quadrant II.

Find the reference angle.

5π4−π=5π4−4π4=π4\frac{5\pi}{4}-\pi=\frac{5\pi}{4}-\frac{4\pi}{4}=\frac{\pi}{4}45π​−π=45π​−44π​=4π​ The angle is in quadrant III

What is the reference angle for 2π3\frac{2\pi}{3}32π​

The angle is in quadrant II, subtract it from π\piπ π−2π3=3π3−2π3=π3\pi-\frac{2\pi}{3}=\frac{3\pi}{3}-\frac{2\pi}{3}=\frac{\pi}{3}π−32π​=33π​−32π​=3π​

Which angle is COTERMINAL to π4\frac{\pi}{4}4π​ ?

Add or subtract 2π2\pi2π to the angle

Which of the following angles are coterminal to the angle −5π3-\frac{5\pi}{3}−35π​ ? Select all that apply.

Add or subtract 2π2\pi2π to the angle

Which of the following angles are coterminal to the angle −3π4-\frac{3\pi}{4}−43π​ ? Select all that apply.

Add or subtract 2π2\pi2π to the angle

Are −3π4-\frac{3\pi}{4}−43π​ and 5π4\frac{5\pi}{4}45π​ coterminal angles?

Add or subtract 2π2\pi2π to the angle and it should give you the other.

Are 15π4\frac{15\pi}{4}415π​ and −3π4-\frac{3\pi}{4}−43π​ coterminal angles?

To find an angle that is coterminal to a given angle, add or subtract _______________ and the given angle.

What is the reference angle for 125°?

180°−125°=55°180\degree-125\degree=55\degree180°−125°=55° The angle is in quadrant II

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$\pi-\frac{13\pi}{18}=\frac{18\pi}{18}-\frac{13\pi}{18}=\frac{5\pi}{18}$ Treat it as if in quadrant II.

$\frac{5\pi}{4}-\pi=\frac{5\pi}{4}-\frac{4\pi}{4}=\frac{\pi}{4}$
The angle is in quadrant III

What is the reference angle for $\frac{2\pi}{3}$

The angle is in quadrant II, subtract it from $\pi$
$\pi-\frac{2\pi}{3}=\frac{3\pi}{3}-\frac{2\pi}{3}=\frac{\pi}{3}$

Which angle is COTERMINAL to $\frac{\pi}{4}$ ?

Add or subtract $2\pi$ to the angle

Which of the following angles are coterminal to the angle $-\frac{5\pi}{3}$ ? Select all that apply.

Add or subtract $2\pi$ to the angle

Which of the following angles are coterminal to the angle $-\frac{3\pi}{4}$ ? Select all that apply.

Add or subtract $2\pi$ to the angle

Are $-\frac{3\pi}{4}$ and $\frac{5\pi}{4}$ coterminal angles?

Add or subtract $2\pi$ to the angle and it should give you the other.

Are $\frac{15\pi}{4}$ and $-\frac{3\pi}{4}$ coterminal angles?

$180\degree-125\degree=55\degree$
The angle is in quadrant II