RADIAN
Definition Of Radian
Radian is a unit used for measuring angles. 1 radian is equal to the angle subtended by the center of the circle by an arc on the circumference which is equal to the radius.
More About Radian
180° = π radians
1 degree = π /180 radians or about 0.01745 radians
1 radian = (π/180)° or about 57.296°
Example of Radian
The full angle is 2 π radians and therefore is 360°.
A right angle is π / 2 radians
A straight angle is π radians.
Video Examples: Radian : What is it?
Solved Example on Radian
Ques: Convert 5/12 π radians to degree measure.
Choices:
A. 75°
B. 15°
C. 180°
D. 432°
Correct Answer: A
Solution:
Step 1: 
π = 
[Use 1 radian = 
.]
Step 2: 75°
Ques: An angle measures 144°. What is its measure in Radian?
Choices:
A. 2π/15
B. 2π/5
C. 12π/15
D. 15π/12
Correct Answer: C
Solution:
Step 1: 1 degree = π/180 radians
Step 2: 144° = 144° π/180 radians = 12π/15 radians
Quick Summary
- Radians are a unit for measuring angles.
- 1 radian is the angle subtended by an arc equal in length to the radius.
- 180° = π radians
- 1 radian ≈ 57.296°
🍎 Teacher Insights
Use visual aids to demonstrate the relationship between the radius and the arc length that defines a radian. Emphasize the importance of using radians in calculus and other advanced mathematics courses.🎓 Prerequisites
- Circles
- Angles
- Degrees
- Circumference
- Pi
Check Your Knowledge
Q1: Convert π/2 radians to degrees.
Q2: Convert 180° to radians.
Frequently Asked Questions
Q: How do you convert from degrees to radians?
A: Multiply the angle in degrees by π/180.
Q: How do you convert from radians to degrees?
A: Multiply the angle in radians by 180/π.