Radian Angle Measures 1 radian the angle needed

Radian Angle Measures • 1 radian = the angle needed for 1 radius of arc length on the circle • still measures the amount of rotation from the initial side to the terminal side. - Distance around a circle is circumference. C = 2 pr -Radians uses the unit circle, so r = 1. This makes the distance around the circle 2 p. Radians often use p to symbolize the angle measure.

II I III IV Quadrants remain the same, but quadrant angles are now in radians. In what quadrant would the terminal side of each of the following angles lie? 2 p 3 -7 p 4 11 p 6 -20 p 3

Finding Coterminal Angles in Radians In degrees: In radians: Add or subtract any multiple of Add or subtract any o 360. multiple of 2 p. *Be careful when adding fractions* Easiest Way: Add the numbers on calculator without the p then insert the p in the final answer.

Examples: Find one positive and one negative coterminal angle to . .

Reference Angle with Radians an acute angle formed by the terminal side of any angle (q) and the x-axis (q should be a positive angle 0 – 2 p) Quadrant II Quadrant I = p - q = q a a Quadrant III Quadrant IV = q - p = 2 p - q

Find the reference angle ( ) of each given angle (q). 1) 2 p/3 2) 7 p/6 3) 11 p/3 4) -4 p/3 5) -13 p/5

I HATE Fractions!