1

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

3.1 Reference Angle

2

Example: Find the reference angle for each angle.

• 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

3

Example: Finding Trigonometric Function Values of a Quadrant Angle

• Find the values of the trigonometric functions for 210.

• Reference angle:

210 – 180 = 30Choose point P on the terminal side of the angle so the distance from the origin to P is 2.

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 1 radian.

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.

180

180

6

Example: Degrees to Radians

• Convert each degree measure to radians.

• a) 60

• b) 221.7

60 60 radia80

n1 3

221.7 221.7 3.896 radians180

7

Example: Radians to Degrees

• Convert each radian measure to degrees.

• a)

• b) 3.25

11

4

18011 11495

4 4

1803.25 3.25 186.2

8

Equivalent Angles in Degrees and Radians

6.2823601.0560

4.71270.7945

3.14180.5230

1.5790000

ApproximateExactApproximateExact

RadiansDegreesRadiansDegrees

6

4

3

2

3

2

9

Equivalent Angles in Degrees and Radians continued

10

Example: Finding Function Values of Angles in Radian Measure

• Find each function value.• a)

• Convert radians to degrees.

• b) 4

tan3

1804 4

tan tan3 3

tan 240

3

4sin

3

4sin sin(240 )

3

sin60

3

2