# 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

= =

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 2*π*

**✓ 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° = 2*π* radians and

180° = *π* radians

**Example 1**

**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

- 5
/4 radians*π* - 91.7°
- 30°
- 2.44 radians

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