Understanding Angles: Definitions, Measures, and Properties

2. Def. An angleis the amount of rotation of a ray about its endpoint. Def. An angle formed by rotation a ray 1/360 of a complete rotation has a measure of one degree, denoted by terminal side vertex initial side Note: We can measure an angle using either in degrees or radians.

3. ANGLES Acute angle - less than 90o Obtuse angle - more than 90o Right angle - 90o Straight angle -180o

4. y terminal side standard position for an angle its vertex is at the origin and its initial side is the positive x-axis x vertex initial side A positive angle has a counterclockwise rotation. A negative angle has a clockwise rotation.

5. Def. A quandrantal angle has its terminal side coinciding with one of the axes when it's in standard position. 90 0 , 360 180 270

6. their measures sum to 180 complementary angles A their measures sum to 90 C

10. Def.A central angle is a positive angle whose vertex is the center of a circle and whose initial and terminal sides intercept the circle forming an arc. θ

11. Def. If a central angle intercepts an arc equal in length to the radius of the circle, it has a measure of 1 radian. r r θ r

12. How many radians can be "cut off" around a circle of radius r? r θ r

19. Right Triangle Pythagorean Theorem c a b hypotenuse is 2 times as long as the short leg and long leg is 3 times as long as the short leg 2 legs are equal and the hypotenuse is 2 times as long as either leg

21. y Coterminal angles angles that when placed in standard position have the same initial and terminal sides 425 65 x -295

22. y x