Lesson 2.8

There are 2 radians in a full rotation -- once around the circle

There are 360° in a full rotation To convert from degrees to radians

or radians to degrees, use the proportion

©Carolyn C. Wheater, 2000 3

degrees

360

radians

2

©Carolyn C. Wheater, 2000 4

Find the degree measure equivalent of radians.

degrees

360

radians

210

360

r

2

2360 420

420

360

7

6

r

r

degrees

360

radians

360

3 4

2

22 270

135

d

d

d

3

4

Find the radian measure equivalent of 210°

Reciprocal Identities

©Carolyn C. Wheater, 2000 5

sincsc

xx

1

cossec

xx

1

tancot

xx

1

tansin

cosx

x

x

cotcos

sinx

x

x

Quotient Identities

The angles whose terminal sides fall in quadrants II, III, and IV will have values of sine, cosine and other trig functions which are identical (except for sign) to the values of angles in quadrant I.

The acute angle which produces the same values is called the reference angle.

©Carolyn C. Wheater, 2000 8

Use the phrase “All Star Trig Class” to remember the signs of the trig functions in different quadrants.

©Carolyn C. Wheater, 2000 9

AllStar

Trig Class

All functions are positive

Sine is positive

Tan is positive

Cos is positive

Describe how to obtain the exact values of cos (π/4) and sin(π/4)

Reference angle: 45 so…

Sin (π/4) =

cos(π/4) =

Find the exact values of cos (5π/6) and sin(5π/6)

150 so Reference angle: 30, quadrant 3

Cos =

Sin = -1/2

Csc 300 - 1/sin =

Sec (11π/6)Ref. angle: 30, 1/cos =

Cot (3π/4) Ref angle: 45, -cos/sin = = -1

Exact: (cos 47.3, sin 47.3)

Hundredth: (.68, .73)

Pages 128 – 129

2-18 evens!