Radian and Degree Measures — Practice Quiz

A Trigonometry cheat sheet for Radian and Degree Measures — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Radians to Degrees

$$1 \text{ rad} = \frac{180^\circ}{\pi} \approx 57.3^\circ$$

Degrees to Radians

$$1^\circ = \frac{\pi}{180} \text{ rad} \approx 0.0175 \text{ rad}$$

Practice quiz

  1. Convert $\frac{\pi}{2}$ radians to degrees.

    • $90^\circ$
    • $180^\circ$
    • $45^\circ$
    • $270^\circ$

    Answer: $90^\circ$

  2. What is the radian equivalent of an angle measuring $180^\circ$?

    • $\pi \text{ rad}$
    • $\frac{\pi}{2} \text{ rad}$
    • $2\pi \text{ rad}$
    • $\frac{3\pi}{2} \text{ rad}$

    Answer: $\pi \text{ rad}$

  3. An angle of $\frac{3\pi}{4}$ radians is equal to how many degrees?

    • $135^\circ$
    • $225^\circ$
    • $45^\circ$
    • $90^\circ$

    Answer: $135^\circ$

  4. Convert $30^\circ$ to radians.

    • $\frac{\pi}{6} \text{ rad}$
    • $\frac{\pi}{3} \text{ rad}$
    • $\frac{\pi}{4} \text{ rad}$
    • $\frac{\pi}{2} \text{ rad}$

    Answer: $\frac{\pi}{6} \text{ rad}$

  5. Approximately how many degrees is $2 \text{ radians}$? (Use the approximation $1 \text{ rad} \approx 57.3^\circ$)

    • $114.6^\circ$
    • $57.3^\circ$
    • $180^\circ$
    • $90^\circ$

    Answer: $114.6^\circ$

  6. Approximately how many radians is $60^\circ$?

    • $1.047 \text{ rad}$
    • $0.524 \text{ rad}$
    • $1.571 \text{ rad}$
    • $0.0175 \text{ rad}$

    Answer: $1.047 \text{ rad}$

  7. If an arc length is equal to the radius of a circle, what is the angle subtended by the arc in radians?

    • $1 \text{ rad}$
    • $\pi \text{ rad}$
    • $2\pi \text{ rad}$
    • $\frac{\pi}{2} \text{ rad}$

    Answer: $1 \text{ rad}$

  8. An angle measures $\frac{5\pi}{6}$ radians. What is this angle in degrees?

    • $150^\circ$
    • $210^\circ$
    • $300^\circ$
    • $120^\circ$

    Answer: $150^\circ$

  9. Convert $270^\circ$ to radians.

    • $\frac{3\pi}{2} \text{ rad}$
    • $\frac{2\pi}{3} \text{ rad}$
    • $\frac{5\pi}{4} \text{ rad}$
    • $\frac{\pi}{2} \text{ rad}$

    Answer: $\frac{3\pi}{2} \text{ rad}$

  10. Which of the following angles is the largest?

    • $60^\circ$
    • $1 \text{ rad}$
    • $50^\circ$
    • $\frac{\pi}{4} \text{ rad}$

    Answer: $60^\circ$

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