1. 13-2 ANGLES AND THE UNIT CIRCLE FIND ANGLES IN STANDARD POSITION BY USING COORDINATES OF POINTS ON THE UNIT CIRCLE.

2. ANGLES An angle is in standard position when the vertex is at the origin and one ray is on the positive x-axis. The ray on the x-axis is the initial side of the angle The other ray is the terminal side of the angle. A positive angle (120⁰) starts on the x-axis and moves counterclockwise A negative angle (-120⁰) starts on the x-axis and moves clockwise

3. PRACTICE

4. REFERENCE TRIANGLES

5. MEASURING ANGLES IN STANDARD POSITION Find the measure of a counterclockwise angle whose terminal side goes through the point (0, 3) Since it is counterclockwise the angle is positive Sketch the angle It is positive 90⁰ Find the measure of a clockwise angle whose terminal side goes through the point (-2, -2) Since it is clockwise the angle is negative Sketch the angle and draw a right triangle Since the sides are the same length, we know the triangle forms a 45⁰ angle -135⁰

6. COTERMINAL ANGLES Two angles in standard position that share the same terminal side. You can find coterminal angles by adding or subtracting multiples of 360⁰ (a complete rotation) 135⁰ and -225⁰ are coterminal since 135⁰ – 360⁰ = -225⁰ Ex: which of the following angles are coterminal? 60⁰ -60⁰ 300⁰ -420⁰ All but 60⁰ are coterminal

7. UNIT CIRCLE

8. PRACTICE

9. ASSIGNMENT Odds p.840 #7-33