1. 7.1 Radian and Degree measure
Objectives:
• Changing Degrees to Radians
• Changing Radians to Degrees

2. Concept: Definition of a Radian
• Radian is the measure of the arc of a circle .
• Unit circle is a circle with a radius of 1.

3. Concept: Definition of a Radian
The circumference of a circle with a radius of “r” is 2πr. Therefore, a full rotation in radian measure is 2π.
360º = 2π
180º = π r

4. Concept: Things That Are Equal
360º = and º =
So or

5. Concept: Converting R = D • where R = radians
Degrees into Radians:
R = D • where R = radians
and D = degrees
Note: You should leave your answer in terms of π.
Ex: Convert 45º to radians
R = 45º • = 45π = π

6. Concept: Converting Ex: Convert 210º degrees to radians. Answer 7π 6
You try:
Ex: Convert 210º degrees to radians.
Answer 7π 6

7. Concept: Converting D = R • where R = radians
Radians to Degrees:
D = R • where R = radians
and D = degrees
Note: In this case, the π usually disappears. If the radian was given to you as a decimal, then you will use 3.14… for π.
Ex: Convert radians to degrees.
D = 7π • = π = 315º π

8. Concept: Converting Ex: Convert 3π radians to degrees. 8 Answer: 67.5º
You try:
Ex: Convert 3π radians to degrees. 8
Answer: 67.5º

9. HOMEWORK
IXL A2:X.1