Questions: Introduction to radians
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. \(\quad 30^\circ\)
1.2. \(\quad 105^\circ\)
1.3. \(\quad 298^\circ\)
1.4. \(\quad 61^\circ\)
1.5. \(\quad 353^\circ\)
1.6. \(\quad 197^\circ\)
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. \(\quad \dfrac{\pi}{3}\)
2.2. \(\quad \dfrac{2\pi}{3}\)
2.3. \(\quad \dfrac{\pi}{7}\)
2.4. \(\quad \dfrac{5\pi}{7}\)
2.5. \(\quad 5\)
2.6. \(\quad \dfrac{3}{4}\)
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 \(\dfrac{\pi}{8}\)
3.2. circle with radius \(\dfrac{1}{3}\) over an angle of \(\dfrac{3\pi}{2}\)
3.3. circle with radius \(30\) over an angle of \(\dfrac{7\pi}{15}\)
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.