Alaina's blog, 6 March 2010

CHAPTER 10 REVIEW
Here are all the formulas to memorize from each section:

10-1

**Sum and difference formulas for cosine and sine:

cos (alpha + or - beta) = cos(alpha)cos(beta) - or + sin(alpha)sin(beta)

sin (alpha + or - beta) = sin(alpha)cos(beta) + or - cos(alpha)sin(beta)

**Use these formuals to rewrite a sum or difference as a product:

sin(x) + sin(y) = 2sin(x+y/2)cos(x-y/2)

sin(x) - sin(y) = 2cos(x+y/2)sin(x-y/2)

cos(x) + cos(y) = 2cos(x+y/2)cos(x-y/2)

cos(x) - cos(y) = -2sin(x+y/2)sin(x-y/2)

10-2

**Sum and difference formulas for tangent:

tan(α) + tan (β)= tan (α)tan (β)/1- tan (α) tan (β)

tan (α)- (β)=tan (α) tan (β)/1+ tan (α) tan (β)

10-3

**Double-angle and half-angle formulas

sin 2(α)== 2sin(α)cos(α)

cos 2(&alpha) = cos^2(α)-sin^2(α)=1-2sin^2(α)=2cos^2(α)-1

tan 2(α)== 2tan(α)/1-tan^2(α)

sin(α/2)= +- √(1-cos(α)/2) cos(α/2)= +- √(1+cos(α)/2)

tan(α/2)= +- √(1-cos(α)/1+cos(α))=sin(&alpha)/1=cos(α)/2

1-cos(α)/sin(α)

**Decimal- use half-angle formula to find alpha. multiply the decimal angle by 2.

I am having trouble knowing when to use what double or half angle formula. I have no clue which one to use because there are soo many similar ones. So if anyone can help me with that i would be happy! I also have trouble doing the problems when you have to make a triangle to find the angle for cos or sine. I dont understand what numbers go on the triangle, which quad the triangle goes in, and what side of the triangle the numbers go on.