Algebra 2 Radians and the Unit Circle Test with Point Values (PDF)

Algebra 2 math test: Radians and the Unit Circle – Maths PDF

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This unit circle test for Algebra 2 covers radians and the unit circle (Common Core F-TF.A.1, F-TF.A.2, F-TF.A.3), with a free PDF to print.

This 45-minute test on radians and the unit circle has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Radians and the Unit Circle
Standards: F-TF.A.1, F-TF.A.2, F-TF.A.3
Time: 45 minutes
Total: 20 points

Unit circle test: questions

Question 1 – Convert angles [2 pts]

Convert \(150^{\circ}\) to radians. (1 point)
Convert \(\frac{5\pi}{3}\) to degrees. (1 point)

Question 2 – Arc length [2 pts]

A sector: s = r times the central angle in radians.

A sector has radius 8 centimeters and central angle \(\frac{5\pi}{6}\). Find the arc length in terms of \(\pi\).

Question 3 – Exact values [3 pts]

Quadrant I: the points (cos θ, sin θ) for the special angles.

Use the unit circle to find each exact value.

\(\sin\frac{\pi}{3}\) (1 point)
\(\cos\frac{\pi}{4}\) (1 point)
\(\tan\frac{\pi}{6}\) (1 point)

Question 4 – Reference angles [3 pts]

Find each exact value.

\(\cos\frac{4\pi}{3}\) (1 point)
\(\sin\frac{11\pi}{6}\) (1 point)
\(\tan\frac{5\pi}{4}\) (1 point)

Question 5 – Solve for the angle [2 pts]

Find all \(\theta\) in \([0, 2\pi)\) with \(\cos\theta = \frac{\sqrt{2}}{2}\).

Question 6 – Coterminal and negative angles [2 pts]

Evaluate \(\sin\frac{9\pi}{4}\) and \(\cos\left(-\frac{2\pi}{3}\right)\).

Question 7 – Point on the unit circle [2 pts]

Two marked angles.

The point \(P\) on the unit circle at angle \(\frac{3\pi}{4}\) is marked. Give its coordinates.

Question 8 – Bike wheel [2 pts]

A bicycle wheel has radius 14 inches. How far does a point on the tire travel when the wheel turns through \(\frac{5\pi}{2}\) radians? Give the exact value and round to the nearest inch.

Question 9 – Find the error [2 pts]

Liam says \(\tan\frac{\pi}{2} = 0\) because \(\cos\frac{\pi}{2} = 0\). Explain the error.

Key facts behind this unit circle test

Key facts

θ = s / r, and 180° = π radians.
Arc length s = rθ when θ is in radians.
Point on the unit circle at θ: (cos θ, sin θ).
tan θ = sin θ / cos θ; cos² θ + sin² θ = 1.
Use reference angles and quadrant signs for exact values.

How to use this unit circle test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

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