2. 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. initial side terminal side angle

3. Basic Terms Positive angle: The rotation of the terminal side of an angle counterclockwise. Negative angle: The rotation of the terminal side is clockwise. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

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

6. Example: Coterminal Angles 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 

8. What’s a radian? You’re used to thinking of a circle in terms of degrees: 360° is the whole circle. 180° is half the circle etc... Radian measure is just a different way of talking about the circle. Just as we can measure a football field in yards or feet--we can measure a circle in degrees or in radians!

9. Think about what the word radian sounds like… it sounds like “radius,” right? It turns out that a radian has a close relationship to the radius of a circle.

10. Converting Between Degrees & Radians 1. Multiply a degree measure by radian and simplify to convert to radians. 2.Multiply a radian measure by and simplify to convert to degrees.

11. Example: Degrees to Radians Convert each degree measure to radians. a)60  b) 221.7 

12. (a) 30° (b) 120° (c)  60° (d) 270° (e) 104 °

13. Example: Radians to Degrees Convert each radian measure to degrees. a) b) 3.25

15. Write these down in your notes! If you memorize them, it will make converting from radians to degrees (and vice versa) much easier!