10-3

10-3 has like a million formulas that we have to learn. So here they are:

1. sin2(alpha) = 2sin(alpha)cos(beta)

2. cos2(alpha) = cos^2(alpha)-sin^2(alpha)

3. cos2(alpha) = 1-2sin^2(alpha)

4. cos2(alpha) = 2cos^2(alpha)-1

5. tan2(alpha) = 2tan(alpha)/1-tan^2(alpha)

6.sin(alpha)/2 = +or- square root of 1-cos(alpha)/2

7. cos(alpha)/2 = +or- square root of 1+cos(alpha)/2

8. tan(alpha)/2 = +or- square root of 1-cos(alpha)/1+cos(alpha)

9. tan(alpha)/2 = sin(alpha)/1+cos(alpha)

10. tan(alpha)/2 = 1-cos(alpha)/sin(alpha)

Ex. 1: Simplify

2cos^2 10degrees-1

First, look at your formulas and see which one would fit the problem. You then see that you can use formula 4 and you replace the alphas with 10 degrees.

cos(2)(10) which is cos 20 degrees. Cos 20 degrees does not exist on the trig chat, therefore you cannot simplify it anymore.

Ex. 2: Simplify

2sin(alpha)/2cos(alpha)/2

First, you look to see what formula you would use for this problem. You can use formula 1. sin2(alpha/2). The twos cancel which leaves uou with sin(alpha)