Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for an unit circle quiz? Then this Precalculus quiz on Radians, Arc Length and the Unit Circle asks 10 multiple-choice questions with instant feedback. Ten multiple-choice questions check conversions, arc length, exact values and signs. Each wrong option comes from a common error, such as the wrong sign for the quadrant or swapping sine and cosine.
Standards: F-TF.A.1, F-TF.A.2, F-TF.A.3, F-TF.A.4 · Level: Grade 12 Precalculus
What this Radians, Arc Length and the Unit Circle quiz checks
- Degrees to radians: multiply by π/180; radians to degrees: multiply by 180/π.
- Arc length s = rθ and linear speed v = rω, with θ in radians.
- The point at angle θ on the unit circle is (cos θ, sin θ).
- Sine is odd, cosine is even; sine and cosine have period 2π, tangent has period π.
- Reference angle gives the size of a value; the quadrant gives its sign.
The 10 questions of the quiz
- Convert 240° to radians.
- Convert 3π/4 radians to degrees.
- A circle has radius 10. What is the arc length for a central angle of 3π/5 radians?
- What is sin(π/6)?
- What is cos θ for the angle shown?
- What is tan(3π/4)?
- What is the reference angle of 7π/6?
- What is cos(−π/4)?
- The point shown lies on the unit circle. What is tan θ?
- A wheel makes 5 revolutions every second. What is its angular speed?
After the quiz
Missed a question? Reread the Radians, Arc Length and the Unit Circle lesson, then take the quiz again. Next, solve the Precalculus worksheet on Radians, Arc Length and the Unit Circle, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.
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