Radian Angle Measures• based on the ratio of the arc length in a circle to its radius
• still measures the amount of rotation from the initial side to the terminal side.
Radians often use to symbolize the
angle measure.
- Distance around a circle is
circumference. C = 2C = 2rr -Radians uses the unit circle, so r = 1.
This makes the distance
around the circle 22.
III
III IV
Quadrants remain the same, but quadrant angles are now in radians.
In what quadrant would the terminal side of each of the following angles lie?
11 6
-7 4
2 3
-20 3
II I IV III
Finding Coterminal Angles in Radians
In degrees:Add or
subtract any multiple of
360o.
In radians:Add or subtract any
multiple of 2. *Be careful when adding
fractions*
Easiest Way: Add the numbers on
calculator without the then insert the in the
final answer.
Examples:
Find one positive and one negative coterminal angle to . 5
2
Find one positive and one negative coterminal angle to .
6
17
Reference Angle with Radians an acute angle formed by the terminal side of any
angle () and the x-axis( should be a positive angle between 0 – 2)
Quadrant I
=
Quadrant II
Quadrant III
=
Quadrant IV
Find the reference angle () of each given angle (
1) 2/3
2)7/6
3)11/3
4)-4/3
5)-13/5
/3
2) /6
/3
4 /3
5 /5