Objective: Convert between degrees and radians. Draw angles in standard form.
Warm up
Fill in the blanks.
An angle is formed by two_____________ that have a common point called the
______________ of the angle.
Positive Angle: Rotate initial
side counter clockwise.
Negative Angle: Rotate initial
side clockwise.
Radian Measure:
The measure of q (theta) in radians of a central angle is equal to the ration
of the length of the intercepted arc (s) to the radius of the circle.
Example 1
A central angle q in a circle of radius 12 ft intercepts an arc of length 42 ft.
What is the radian measure of q .
Degrees and Radians
Convert:
• Degrees to radians. Multiply by
p
180 0
• Radians to degrees. Multiply by 180
p
Example 2
Convert each angle in degrees to radians.
a. 60 0
b.
270 0
c. -300 0
0
Example 3
Convert each angle in radians to degrees.
a. p
4
b. - 4p
3
c. 6
Example 4
Draw the angle in standard form.
a.
q = 30 0
b. q = -
p
4
c.
q = 270 0
d.
q = 900 0
e. q =
7p
4