Will Teach you all of you angels how to Angle properly! Angle Measurement Mr. Peter Richard Will Teach you all of you angels how to Angle properly! Learning Goals: Extend the definition of an angle to include negative angles and angles greater than 180°

Definition y x Terminal Side Vertex A Angle A is in standard position Initial Side

Definition If the terminal side moves counter-clockwise, angle A is positive y A x

Definition If the terminal side moves counter-clockwise, angle A is positive y A x

Definition If the terminal side moves counter-clockwise, angle A is positive y x A

Definition If the terminal side moves clockwise, angle A is negative y x A

Definition If the terminal side moves clockwise, angle A is negative y x A

Definition If the terminal side moves clockwise, angle A is negative y x A

Definition If the terminal side moves clockwise, angle A is negative x y A

Definition y If the terminal side is on an axis, angle A is a quadrantel angle A x

Definition y If the terminal side is on an axis, angle A is a quadrantel angle A x

Definition y If the terminal side is on an axis, angle A is a quadrantel angle A x

Try This What kind of angle is this? (hint: where is the terminal side?) quadrantal angle

Try This What is the measure of this angle? -90° -45° -270° -360°

Try This What is the measure of this angle? -90° -45° -270° -360°

Try This What is the measure of this angle? 0° 45° 90° 120° 180°

Try This What is the measure of this angle? 0° 45° 90° 120° 180°

Try This What is the measure of this angle? -90° -45° -270° -360°

Try This What is the measure of this angle? -90° -45° -270° -360°

Try This What is the measure of this quadrantal angle? x y 0°

Try This If a 143° angle is in standard position, determine the quadrant in which the terminal side lies. x y 2

Try This If a 280° angle is in standard position, determine the quadrant in which the terminal side lies. x y 4

Definition Coterminal Angles: Angles that have the same terminal side.

Example Find positive angles and negative angles that are coterminal with 30°.

Important Idea To find coterminal angles, simply add or subtract 360° to the given angle or any coterminal angle.

30° x y Analysis 30° and 390° have the same terminal side, therefore, the angles are coterminal y 390° x

30° x y Analysis 30° and 750° have the same terminal side, therefore, the angles are coterminal x y 750°

30° x y Analysis 30° and 1110° have the same terminal side, therefore, the angles are coterminal x y 1110°

30° x y Analysis 30° and -330° have the same terminal side, therefore, the angles are coterminal x y -330°

With Mr. Peter Richard How many angles can you find that are coterminal with a 30° angle and how do you find them?

Try This Find 3 angles coterminal with 60° 420°,780° and -300°

Practice Quiz: Page 722: # 2, 4, 6, 8, 12 Homework: # 1, 3, 5, 11, 15