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
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 \(\sin\theta=\frac{5}{13}\) and \(\theta\) is in Quadrant II, what is \(\cos\theta\)?
A
\(\frac{12}{13}\)
B
\(-\frac{5}{12}\)
C
\(-\frac{8}{13}\)
D
\(-\frac{12}{13}\)
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!
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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: \(\sin^{2}\theta+\cos^{2}\theta=1\).
See every chapter on the Algebra 2 math page.