10-3

Lesson 10-3 was about using Double Angle/Half Angle formulas. This lesson included 10 new formulas that needed to be learned in order to solve these problems. You could easily write down the formulas on note cards to study or if you're like me and learn by doing things, then you can just keep doing example problems until you remember the formulas.

The formulas included:

1. sin2alpha= 2sinalphacosalpha

2. cos2alpha= cos^2A-sin^2A

3. sin2alpha= 1-2sin^2A

4. sin2alpha= 2cos^2alpha-1

5. tan2alpha= 2tanalpha/1-tan^2alpha

6. sin alpha/2= +/- square root of 1-cosalpha/2

7. cos alpha/2= +/- square root of 1+ cosalpha/2

8. tan alpha/2= +/- square root of 1-cosalpha/1+cosalpha

9. square root of 1-cosalpha/1+cosalpha= sinalpha/1+cosalpha

10. sinalpha/1+cosalpha= 1-cosalpha/sinalpha

Example problem using a formula:

1. 2cos^2 10 degrees-1

-This example problem represents the formula sin2alpha= 2cos^2alpha-1

-Becomes cos2(10) which equals cos20degrees

Example problem number 2 using a formula:

2. 2 sin alpha/2 cos alpha/2

-This example problem represents the formula sin2alpha= 2sinalphacosalpha

-Becomes sin2 (alpha/2); the 2's cancel out and you're left with sinalpha.