Convert Angles Between Degrees and Radians

Practice converting angle measures from degrees to radians and from radians to degrees. Full step-by-step solutions are provided at the bottom of the page.

Multiple Choice Questions

Question 1

What is the measure in degrees of the angle \[ A = \frac{7\pi}{6} ? \]

  1. \(150^\circ\)
  2. \(210^\circ\)
  3. \(100^\circ\)
  4. \(120^\circ\)

Question 2

What is the measure in radians of the angle \[ A = 330^\circ ? \]

  1. \(\frac{11\pi}{3}\)
  2. \(\frac{7\pi}{4}\)
  3. \(\frac{7\pi}{6}\)
  4. \(\frac{11\pi}{6}\)

Question 3

What is the measure in degrees of the angle \[ A = \frac{21\pi}{5} ? \]

  1. \(756^\circ\)
  2. \(710^\circ\)
  3. \(36^\circ\)
  4. \(420^\circ\)

Question 4

What is the measure in radians of the angle \[ A = -750^\circ ? \]

  1. \(-\frac{25\pi}{6}\)
  2. \(\frac{25\pi}{6}\)
  3. \(-\frac{15\pi}{6}\)
  4. \(-\frac{35\pi}{6}\)

Question 5

What is the degree measure of the angle \[ A = -\frac{15\pi}{2} ? \]

  1. \(135^\circ\)
  2. \(1350^\circ\)
  3. \(-90^\circ\)
  4. \(-1350^\circ\)

Step-by-Step Solutions

Question 1 Solution

To convert radians to degrees, multiply by \( \frac{180^\circ}{\pi} \):

\[ \frac{7\pi}{6} \times \frac{180^\circ}{\pi} = 7 \times 30^\circ = 210^\circ \]

Correct answer: b) \(210^\circ\)

Question 2 Solution

To convert degrees to radians, multiply by \( \frac{\pi}{180^\circ} \):

\[ 330^\circ \times \frac{\pi}{180^\circ} = \frac{11\pi}{6} \]

Correct answer: d) \( \frac{11\pi}{6} \)

Question 3 Solution

\[ \frac{21\pi}{5} \times \frac{180^\circ}{\pi} = 21 \times 36^\circ = 756^\circ \]

Correct answer: a) \(756^\circ\)

Question 4 Solution

\[ -750^\circ \times \frac{\pi}{180^\circ} = -\frac{750\pi}{180} = -\frac{25\pi}{6} \]

Correct answer: a) \(-\frac{25\pi}{6}\)

Question 5 Solution

\[ -\frac{15\pi}{2} \times \frac{180^\circ}{\pi} = -15 \times 90^\circ = -1350^\circ \]

Correct answer: d) \(-1350^\circ\)

More Trigonometry Problems with Solutions

More Trigonometry Problems with Full Solutions