3.1 Reference Angle

1. 3.1 Reference Angle • A reference angle for an angle  is the positive acute angle made by the terminal side of angle  and the x-axis.

2. a) 218 Positive acute angle made by the terminal side of the angle and the x-axis is 218  180 = 38. 1387 Divide 1387 by 360 to get a quotient of about 3.9. Begin by subtracting 360 three times. 1387 – 3(360) = 307. The reference angle for 307 is 360 – 307  = 53 Example: Find the reference angle for each angle.

3. Find the values of the trigonometric functions for 210. Reference angle: 210 – 180 = 30 Choose point P on the terminal side of the angle so the distance from the origin to P is 2. Example: Finding Trigonometric Function Values of a Quadrant Angle

4. An angle with its vertex at the center of a circle that intercepts an arc on the circle equal in length to the radius of the circle has a measure of 1radian. 3.2 Radians and Degrees

5. Converting Between Degrees and Radians • 1. Multiply a degree measure by radian and simplify to convert to radians. • 2. Multiply a radian measure by and simplify to convert to degrees.

6. Example: Degrees to Radians • Convert each degree measure to radians. • a) 60 • b) 221.7

7. Example: Radians to Degrees • Convert each radian measure to degrees. • a) • b) 3.25

8. Degrees Radians Degrees Radians Exact Approximate Exact Approximate 0 0 0 90 1.57 30 .52 180  3.14 45 .79 270 4.71 60 1.05 360 2 6.28 Equivalent Angles in Degrees and Radians

9. Equivalent Angles in Degrees and Radians continued

10. Find each function value. a) Convert radians to degrees. b) Example: Finding Function Values of Angles in Radian Measure