7-3 Identities Day 1

Identities Identities are like _______________________ We will work on one side only. Usually the HARDER looking side. If there are fractions ____________________ ______________if it helps!

Need to remember:

Examples

Need some hints? Choose harder side. Tossup? Try the left side. Fractions? ___________________. __________, if it helps. One side in many functions/ other side in one? Work on the ______________ side and get it into the only function seen on the other side.

Angle Addition/Subtraction 7-4 Formulas Angle Addition/Subtraction

Lets try an experiment? What is ? Is it equal to This demonstrates that trigonometric functions ____________________________ Imagine

The Formulas Based on Geometry and distance Formula

The Formulas Based on Geometry and distance Formula

What do these formulas do? Essentially give you the option of 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. Going backwards, and “compressing” an expanded formula into a form you can solve.

Examples Find the following 1.

Prove by angle addition formulas.

Example 7. Given , and Find

Class Work Find the following 4. 5. 6.

Double Angle Half Angle 7-5 More Formulas Double Angle Half Angle

Lets derive some formulas: What is ? What is

Some other versions

Example Evaluate sin 60 using double angles.

If and find 5 13 -12

Find b 4 b Θ Θ 2

Half Angle Formulas

Examples 1. Evaluate sin 15 using half angle.

If and find

Find