7-4 Formulas

Angle Addition/Subtraction

Lets try an experiment?What is ?

Is it equal to

This demonstrates that trigonometric functions are not distributive.

Imagine

cos 30 60

cos30 cos60 ?

(4 9)

The FormulasBased on Geometry and distance

Formula

sin A B sinAcosB cosAsinB

cos A B cosAcosB sinAsinB

cos A B cosAcosB sinAsinB

sin A B sinAcosB cosAsinB

The FormulasBased on Geometry and distance

Formula

tanA tanBtan A B

1 tanAtanB

tanA tanBtan A B

1 tanAtanB

What do these formulas do?

Essentially give you the option of a) finding the sin/cos of an angle that

can be made up of two angles you know. While you don’t know the cos 75 °, you know that 75° is made up of two angles that you know.

b) Going backwards, and “compressing” an expanded formula into a form you can solve.

Examples

Find the following1.

2. Prove by angle addition formulas.

3.

cos75

cos202 cos22 sin202 sin22

sin90 1

ExamplesFind the following

4.

5.

6.

sin15

tan105

cos225

Examples

7. Given ,

and

Find

3cos

5

8sin

17

30 ,

2 2

sin( ), cos( ), Quad of ( )