Part 1

 We interpret an angle as a rotation of the ray R 1 onto R 2.  An angle measure of 1 degree is formed by rotating the initial side th of a complete revolution.

 If a circle of radius 1 is drawn with the vertex at the center, the measure of this angle in radians (rad) is the length of the arc that subtends the angle. Radian measure is a unitless number.

 If the radius = 1 then the circumference of a circle is 2π so a complete revolution around the circle is 2 π radians.  A straight angle has measure π radians or 180 degrees.  A right angle has measure ____ radians.

60° = ____ radians 120° = ____ radians -45 ° = _____ radians 1 ° = _____ radians To convert from degrees to radians, multiply by

To convert from radians to degrees, multiply by ⅚ π = ____ ° -3/2 π = ____ ° 1 rad = _____ °

 An angle in standard position is drawn in a rectangular coordinate system by placing the vertex at the origin and the initial side on the positive x-axis, then rotating the ray CCW (+ °) rotations or CW (- °) rotations.

 Two angles in standard position are coterminal if their sides coincide. (which two graphs from previous slide are coterminal?)  Hint: they must have the same initial and terminal sides but different angle measure. Both angles can be positive or one can be positive and one can be negative.  Two positive coterminal angles differ by one full rotation. An angle has infinitely many coterminal angles found by :

 Θ = 45° Θ = ⅓ πΘ = - ⅓ π  Find angles between 0 and 360 that are coterminal with 1635 °.  Find angles between 0 and 2 π that is coterminal with 88/3 π.

Homework