Algebra 2 13.2A Angles and Angle Measure Obj: able to change degree measure to radian measure and vice versa, able to identify coterminal angles

y An angle of rotation is determined by rotating a ray about its endpoint, or vertex . The starting position of the ray is the initial side of the angle. The position after rotation is the terminal side . Terminal side θ x In standard position , the vertex of the angle in the coordinate plane is at the origin, and the initial side is the positive x-axis. Initial side

The measure of an angle is determined by the amount of rotation from the initial side to the terminal side.

1 A measure of one degree (1a ) is equivalent to of a full revolution. 360 Positive angles are generated by counterclockwise rotation , and negative angles by clockwise rotation . Two angles are coterminal if they have the same initial and terminal sides.

Two positive angles are complementary if the sum of their measures is 90 degrees.

Two positive angles are supplementary if the sum of their measures is 180 degrees.

Draw an angle in standard position . 1. 210 ° 2. −150 ° 3. 390 °

Unit Circle (Radius 1) One Radian is the measure of an angle θ whose terminal side intercepts an arc of length 1 on the unit circle. y

The radian measure of θ , the arc length s, and the radius r are related by the equation s = rθ . s = 1θ

Positive angles are generated by counterclockwise rotation , & negative angles by clockwise rotation . 1 x Two angles are coterminal if they have the same initial and terminal sides. θ π 1 Two positive angles are complementary if the sum of their measures is radians (or 90 degrees). 2 π Two positive angles are supplementary if the sum of their measures is radians (or 180 degrees).

A measure of 2π radians = 360 ° .

Conversions Between Degrees and Radians π radians To rewrite degrees as radians, multiply by . When no units of angle measure are specified, radian measure is implied. a 180 180 a To rewrite radians as degrees, multiply by . For instance, θ = 2 means θ = 2 radians. π radians

Rewrite each angle measure in radians . Rewrite each angle measure in degrees . 5π 4. 240a 5. − 80 a 6. 1 radian 7. radians 6

Find one angle with positive measure and one angle with negative measure coterminal with each angle . (Add or subtract multiples of 360 a or 2π radians ) π 8. 15 a − radians 9. 4

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