Bell Ringer (12-8-14) Using any available source define: 1. Radian 2. Standard Position 3. Coterminal 4. Intercepted Arc 5. Reference Angle 6. Unit Circle.

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Presentation transcript:

Bell Ringer ( ) Using any available source define: 1. Radian 2. Standard Position 3. Coterminal 4. Intercepted Arc 5. Reference Angle 6. Unit Circle

Radians and the Unit Circle Monday, December 8, 2014

What is a radian? A radian is the measure of an angle determined by joining the center of a circle to the endpoints of an arc that is equal in length to the radius of the circle.

How do we convert? Since everything to do with circles is proportional… angle in degrees = angle in radians 360 2π 360 2πOr…..

Examples: Convert the following degrees to radians:    Convert the following radians to degrees: 4. π5. 7π6. π

Unit Circle Info. A circle with a radius of 1 unit is called the Unit Circle. In the unit circle, angles are measured from the x-axis. Positive angles are measured counterclockwise and negative angles are measured clockwise. Angles in standard position are coterminal if they share the same terminal side.

Examples: Find one angle with a positive measure and one angle with a negative measure coterminal with the given angle    10. 6π π12. 8π 5 2 7

Central Angle and Intercepted Arc When a central angle, , of a circle with radius r is measured in radians, then length of the intercepted arc, s, is given by the equation: s = r 

Examples: 3π 13. r = 12m,  = 3π Find the length of the intercepted arc if the radius is 3cm and the central angle is 60 .

Unit Circle Fill in indicated degree and radian measure for the Unit Circle.

Practice Radians, Degrees, and Coterminal Angles ClassworkHomework