Online Trigonometry Tutoring: Radian and Degree Measures

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Learn about radian and degree from certified online trigonometry tutor.

Radian and Degree Measures

Measure of an angle is determined by the amount of rotation from the initial side to the terminal side.
Many mathematical calculations in Geometry use degrees to measure and calculate angles.
Degree measures are used in many practical applications in building and architecture that use

$\theta$ = $\frac{s}{r}$ = $\frac{length of subtendedarc}{length of radius}$

A radian is the measure of a central angle q that intercepts an arc ‘s‘ equal in length to the radius ‘r‘ of the circle.

✓ Radian is the measure of an angle that, when drawn as a central angle of a circle, intercepts an arc whose length is equal to the length of the radius of the circle.

✓ Radian measure for a full circle is 2π

✓ In radians, one complete counterclockwise revolution is 2π

✓ Degrees are used to measure direction and angle size

✓ Full circle = 360°.

✓ in degrees, one complete counterclockwise revolution is 360°.

So, degree and radian measure are related by the equations.

360° = 2π radians and

180° = π radians

Example 1

Converting from Degree to Radians = multiply by π/180

Convert 70 degrees to radians

Solution: 70 x π/180

= 70 x 3.14/180 (π = 3.14)

= 1.221 radians

Converting from Radians to Degrees = multiply by 180/π

Convert 14 radians to degrees

Solution: 14 × 180/π

= 14 × 180/3.14

= 802.54 degrees

Checkpoint

Problem 1. Find the radian measure of 225° .

Problem 2. Express 1.6 radians to degrees.

Problem 3. Convert π/6 radians to degrees.

Problem 4. Convert 140° to radian measure.

Answer Key

5π/4 radians
91.7°
30°
2.44 radians

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