1. 13.2 Angles and Angle Measure
Objectives:
Change radian measure to degree measure and vice-versa.
Identify coterminal angles.

2. Angles on a coordinate plane
Parts of an angle on a coordinate plane: Initial side – a ray fixed along the positive x-axis Terminal side – the other ray that can rotate about the center Standard Position – when the vertex is at the origin and the initial side is on the positive x-axis

3. Types of measures
Positive Angle 225°
Negative Angle -135°

4. Angles more than 360°
For each revolution, add 360°, plus the other angle. The angle is 130°+360°= 490°.

5. Drawing Angles
Draw an angle with the given measure in standard position.
210°
540°
=180
3. -45°

6. Radians Radian measure is another unit used to measure angles.
It is based on the concept of a unit circle which is a circle with a radius of 1 whose center is at the origin.
If the radius is 1, the circumference is 2π so 2π is the same as 360°. Smaller angles are fractional parts of 2π.

7. Unit Circle

8. Changing from radians to degrees or from degrees to radians
Radians to degrees – Multiply the number of radians by Example:
Degrees to radians – Multiply the number of degrees by Example: 75°

9. Coterminal Angles
Coterminal Angles are angles in standard position with the same terminal side such as 30° and 390°. To find additional angles with the same coterminal angle, add multiples of 360 or subtract multiples of 360. For radian measure, add multiples of 2π or subtract multiples of 2π.

10. Example:
Find one angle with positive measure and one angle with negative measure coterminal with each angle.
210°
=570°
=-150° 2.

11. Homework p even