9-2: Addition and Subtraction IdentitiesLearning Goals:

•Use the addition and subtraction identities for sine, cosine & tangent

©2009 Roy L. Gover (www.mrgover.com)

ReviewFind the exact values:

1. sin 2. cos1802

3. sin 4. sin 270

35. cos 6. cos

2 2

Review

60°

30°

1

23 45°

45°

1

1

2

Review

1

23 1

1

2

π

6

π

3

π

4π

4

ReviewFind the exact values:

1. sin 30 2. tan6

3. cos 45 4. sin3

55. cos 6. tan220

4

Does cos 40°+ cos 10°=cos 50°?

Analysis

Inquiring Minds Want To Know…

cos(+)=cos cos-sin sincos(-)=cos cos+sin sin

Addition & Subtraction Identities for Cosine:

Important Idea

cos( )

cos cos sin sin

Example

Find the exact value of cos 75° using the values of the function for 30° and 45°

ExampleFind the exact value of

cos using the

values of the function

for

and

π

3π

4

7π

12

Try ThisFind the exact value of cos 15° using the values of the function for 60° and 45°. Hint: cos 15°=cos(60°-45°)

2 6

4 4

Try ThisFind exact value of cos

using the values of the

function for and . Hint:

cos =

cos2 6

4 4

π

12

π

3π

4π

12

π π

3 4

Example

Rewrite the given expression in terms of sin x and/or cos x: cos(x + )

π

sin(+)=sin cos+cos sinsin(-)=sin cos - cos sin

Addition & Subtraction Identities for Sine:

Important Idea

sin( )

sin cos cos sin

Example

Find the exact value of sin 75°. Simplify your answer.

Example

Find exact value of sin

Hint:

Simplify your answer.

13π

12 5π π 13π

4 6 12

Try This

Find exact value of sin

Hint:

5π

12 2π π 5π

3 4 12

Simplify your answer.

6 2

4

Try ThisVerify the identity:

sin(270°+x)=-cos x

Solutionsin(270 )

sin 270 cos cos 270 sin

1(cos ) 0(sin )

cos

x

x x

x x

x

tan tantan( )

1 tan tan

tan tan

tan( )1 tan tan

Addition & Subtraction Identities for Tangent…

Important Idea

tan tantan( )

1 tan tan

Addition & Subtraction Identities for Tangent-the condensed form:

Important Idea

Example

Find the exact value of tan 15° using the values of the tan function for 45° and 30°. Simplify your answer.

Try This

If sin A= & cos B= ,

find tan(A+B).

4

5

3

5

24

7

Lesson Close

Describe a method for finding the exact value of sin 105°.