Algebra 2 Trig Unit Circle Quiz – Free PDF

Contents

This algebra 2 trig unit circle quiz asks 10 multiple-choice questions on radians and the unit circle, and each answer comes with a short explanation.

Ten multiple-choice questions check radian conversion, arc length, unit circle coordinates, exact values and the Pythagorean identity. Pick the single best answer; each explanation points out the common mistake.

Algebra 2Common Core: F-TF.A.1 · F-TF.A.2 · F-TF.C.8

🎯 Radians and the Unit Circle – Algebra 2 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

What is \(135^{\circ}\) in radians?

A \(\frac{3\pi}{2}\)

B \(\frac{3\pi}{4}\)

C \(\frac{5\pi}{4}\)

D \(\frac{2\pi}{3}\)

Question 2

Find the arc length \(s\) of the sector.

Radius 5 inches, angle \(\frac{3\pi}{5}\).

A \(\frac{3\pi}{5}\text{ in}\)

B \(15\pi\text{ in}\)

C \(\frac{25\pi}{3}\text{ in}\)

D \(3\pi\text{ in}\)

Question 3

What are the coordinates of the point on the unit circle for the angle shown?

Angle \(\frac{5\pi}{6}\).

A \(\left(-\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)\)

B \(\left(\frac{\sqrt{3}}{2},\ -\frac{1}{2}\right)\)

C \(\left(-\frac{\sqrt{3}}{2},\ \frac{1}{2}\right)\)

D \(\left(-\frac{\sqrt{3}}{2},\ -\frac{1}{2}\right)\)

Question 4

What is \(\cos\frac{4\pi}{3}\)?

A \(-\frac{1}{2}\)

B \(\frac{1}{2}\)

C \(-\frac{\sqrt{3}}{2}\)

D \(\frac{\sqrt{3}}{2}\)

Question 5

What is \(\tan\frac{5\pi}{6}\)?

A \(\frac{\sqrt{3}}{3}\)

B \(-\frac{\sqrt{3}}{3}\)

C \(-\sqrt{3}\)

D \(-\frac{1}{2}\)

Question 6

If \(\sin\theta=\frac{8}{17}\) and \(\theta\) is in Quadrant II, what is \(\cos\theta\)?

A \(\frac{15}{17}\)

B \(-\frac{8}{15}\)

C \(-\frac{9}{17}\)

D \(-\frac{15}{17}\)

Question 7

What is the reference angle for \(\frac{11\pi}{6}\)?

A \(\frac{\pi}{3}\)

B \(\frac{\pi}{6}\)

C \(\frac{5\pi}{6}\)

D \(\frac{\pi}{12}\)

Question 8

In Quadrant IV, \(\sin\theta=-0.6\). What is \(\cos\theta\)?

A \(-0.8\)

B \(0.4\)

C \(0.8\)

D \(0.64\)

Question 9

Which labeled point has \(\sin\theta< 0\) and \(\cos\theta>0\)?

Four points on the unit circle.

A Point A

B Point B

C Point C

D Point D

Question 10

Which two angles in \(0\le\theta< 2\pi\) satisfy \(\cos\theta=\frac{\sqrt{2}}{2}\)?

The line \(x=\frac{\sqrt{2}}{2}\).

A \(\frac{\pi}{4}\text{ and }\frac{7\pi}{4}\)

B \(\frac{\pi}{4}\text{ and }\frac{3\pi}{4}\)

C \(\frac{3\pi}{4}\text{ and }\frac{5\pi}{4}\)

D \(\frac{\pi}{4}\text{ and }\frac{5\pi}{4}\)

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

\(\theta=\frac{s}{r}\), so \(180^{\circ}=\pi\) radians and \(360^{\circ}=2\pi\) radians.
Arc length is \(s=r\theta\) when \(\theta\) is in radians.
The unit circle point at angle \(\theta\) is \((\cos\theta,\ \sin\theta)\).
Use the reference angle and the quadrant signs to evaluate any angle.
Pythagorean identity: \(\sin^{2}\theta+\cos^{2}\theta=1\).