# Online TrigonometryÂ Tutoring: Radian and Degree Measures

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## Learn about radian and dregree 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*Â that intercepts an arc ‘*s*‘ equal in length to the radius ‘*r*‘ of the circle.

**âœ“ Â 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.

**âœ“ Â **Radian measure for a full circle is 2Ï€

**âœ“ Â **In radians, one complete counterclockwise revolution is 2*Ï€ *

**âœ“ Â Degrees** are used to measure direction and angle size

**âœ“ Â **Full circle = 360Â°.

**âœ“ Â **in degrees, one complete counterclockwise revolution is 360Â°.

### So, degreeÂ and radian measure are related by the equations.

360Â° = 2*Ï€* radians and

180Â° = *Ï€* radians

### Example 1

**Converting from Degree to Radians = multiply by Ï€**/

**180**

**Â Â Â Â Â Convert 70 degrees to radians**

Solution: 70 x *Ï€*/180

= 70 x 3.14/180 (*Ï€* = 3.14)

= 1.221 radians

**Converting fromÂ Radians to Degrees = multiply by 180/ Ï€**

Convert 14 radians to degrees

**Solution: **14 Ã— 180/*Ï€*

= 14 Ã— 180/3.14

= 802.54 degrees

### Checkpoint

**Problem 1. Find the radian measure of 225****o.**

**Problem 2. Express 1.6 radians to degrees. **

**Problem 3. Convert **p**/6 radians to degrees. **

**Problem 4. Convert 140Â° to radian measure.**

**Answers :**

- 5
/4 radians*Ï€* - 91.7Â°
- 30Â°
- Â 2.44 radians

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