# What Is A Radian? 1 radian = the arc length of the radius of the circle.

## Presentation on theme: "What Is A Radian? 1 radian = the arc length of the radius of the circle."— Presentation transcript:

Radian Angle Measures based on the ratio of the arc length in a circle to its radius still measures the amount of rotation from the initial side to the terminal side. Radians often use  to symbolize the angle measure.  C = 2  r - Distance around a circle is circumference. C = 2  r -Radians uses the unit circle, so r = 1. This makes the distance 2  around the circle 2 .

III IIIIV    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? 11  6 -7  4 2  3 -20  3     II I IV III

Finding Coterminal Angles in Radians In degrees: Add or subtract any multiple of 360 o. In radians: Add or subtract any multiple of 2 . *Be careful when adding fractions* Easiest Way: Add the numbers on calculator without the  then insert the  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 (  ) and the x-axis (  should be a positive angle between 0 – 2  )   Quadrant I  =  Quadrant II  Quadrant III  =  Quadrant IV 

Find the reference angle (  ) of each given angle (  1) 2  /3 2)7  /6 3)11  /3 4)-4  /3 5)-13  /5  /3 2)  /6  /3  /3  /5

I HATE Fractions!