Questions: Introduction to radians

Summary

Questions relating to the introduction to radians study guide.

Before attempting these questions, it is highly recommended that you read Guide: Introduction to radians.

Q1

Convert the following angle measures in degrees into radians, giving your answer as both a fraction of $\pi$ and a real number to three decimal places.

1.1. ${30}^{\circ }$

1.2. ${105}^{\circ }$

1.3. ${298}^{\circ }$

1.4. ${61}^{\circ }$

1.5. ${353}^{\circ }$

1.6. ${197}^{\circ }$

Q2

Convert the following angle measures in radians into degrees. If your answer is a decimal, you should give your answer to three decimal places.

2.1. ${\displaystyle \frac{\pi }{3}}$

2.2. ${\displaystyle \frac{2\pi }{3}}$

2.3. ${\displaystyle \frac{\pi }{7}}$

2.4. ${\displaystyle \frac{5\pi }{7}}$

2.5. $5$

2.6. ${\displaystyle \frac{3}{4}}$

Q3

Find the length of arc and the area of the sector of the following specified objects, giving your answer as either a fraction of $\pi$ or expressing your answer to three decimal places.

3.1. circle with radius $7$ over an angle of ${\displaystyle \frac{\pi }{8}}$

3.2. circle with radius ${\displaystyle \frac{1}{3}}$ over an angle of ${\displaystyle \frac{3\pi }{2}}$

3.3. circle with radius $30$ over an angle of ${\displaystyle \frac{7\pi }{15}}$

---

After attempting the questions above, please click this link to find the answers.

---

Version history and licensing

v1.0: initial version created 08/23 by Mark Toner, Ifan Howells-Baines as part of a University of St Andrews STEP project.

• v1.1: edited 05/24 by tdhc.

This work is licensed under CC BY-NC-SA 4.0.