ANGLES & ANGLE MEASURES

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Presentation transcript:

ANGLES & ANGLE MEASURES

NOTE: Clockwise: Negative Counterclockwise: Positive TERMINAL SIDE Clockwise (Negative) INITIAL SIDE Counterclockwise (Positive)

Radian measures are based on a Unit Circle which has a radius of 1. C (circumference)= 2πr and C = 360˚ 2πr = 360˚ 2π radians = 360 degrees

the positive x-axis and the vertex is at the origin. Standard Position: An angle is in standard position if the initial side is the positive x-axis and the vertex is at the origin. Coterminal Angles: Angles that have the same terminal side, but different measures (ex: 30˚ and 390˚, which is 360˚ + 30˚… …they both look alike, but 390˚ has actually gone all the way around once plus a little farther.) 30˚ angle 390˚ angle

Reference Angle: An angle between 0˚ and 90˚ “Back in the day” before calculators were so prevalent, people used trig tables Which had the sin, cos, and tan for angles between 0˚ & 90˚. Ex: 300˚ is a 60˚ in Quad. IV, so the reference angle for 300˚ is 60˚. Ex: -135˚ is a 45˚ in Quad. III, so the reference angle for -135˚ is 45˚.

To change from DEGREES to RADIANS: To change from RADIANS to DEGREES: Degrees =

Ex: 36˚= Ex: 33.75˚ -1020˚ Ex: Ex: -820° =