1. 12.2 – Angles and Angle Measure

2. Standard Position – when the vertex of the angle is at the origin and one ray is on the positive x-axis. Initial Side – the ray on the x-axis. (where the angle starts.) Terminal Side - the ray that rotates about the center. (where the angle ends.)

4. Example 1: Draw an angle with the given measure in standard position. a. 210° b. –45°

5. Example 2: a. In a springboard diving competition, a diver made a 900-degree rotation before slicing into the water. Draw an angle in standard position that measures 900°.

6. Example 2: b. While riding down the mountain, a snowboarder goes off a jump and turns 600° before touching down onto the snow again. Determine how many degrees past the positive x-axis the snowboarder lands.

7. Coterminal Angles: - Two or more angles in standard position with the same terminal side. - How can we find coterminal angles???

8. Example 3: Find an angle with a positive measure and an angle with a negative measure that are coterminal with each angle. b. 210° b. –120°

9. Radians:

11. Example 4: Conversions a. Rewrite 30° in radians. b. Rewrite 120° in radians.

12. Example 5: Conversions

14. - Central Angle – an angle with a vertex at the center of the circle.

15. Example 6: a. The steering wheel on a monster truck has a radius of 11 inches. How far does a point on the steering wheel travel if the wheel makes four fifths of a rotation?

16. Example 6: b. The steering wheel on a yacht has a radius of 16 inches. How far does a point on the steering wheel travel if the wheel makes five sevenths of a rotation?