1. Warm Up Give radian measure for each: 90º b) 120º c) 135º
Find the missing side lengths using trig!
a) b) 1 1 y
45º x
60º

2. Coterminal Angles

3. Basic Terms An angle is formed by rotating a ray around its endpoint.
The ray in its starting position is called the initial side of the angle.
The ray’s location after the rotation is the terminal side of the angle.
terminal side
angle
initial side

4. Basic Terms
Positive angle: The rotation of the terminal side of an angle counterclockwise.
Negative angle: The rotation of the terminal side clockwise.

5. A complete rotation of a ray results in an angle measuring 360.
We don’t have to stop there!
137 more
137 is coterminal with 497. They have the same terminal side! We can keep adding or subtracting 360 to get more coterminal angles.
360
497 altogether!

6. Example 2: For the angles below, find the smallest positive coterminal angle.
(Add or subtract 360 as may times as needed to obtain an angle with measure greater than 0 but less than 360.) a) 1115 b) 187 a) 1115° - 360° - 360° - 360° = 35° b) 187 + 360 = 173

7. THE UNIT CIRCLE

9. This circles has a radius of 1.
(1,0)
(0,1)
(0,-1)
(-1,0)
We call this the unit circle because the radius is one unit.

10. Lets label the angles first

11. Now let’s label them in Radians

12. Let’s fill in the coordinates

13. Homework
STUDY UNIT CIRCLE!!!!!!!!!!! Coterminal Angles Practice