10-3 Simplify

This week in advanced math we learned chapter 10-3 and 10-4 along with reviewing chapter 10 and testing on it. In 10-1 you have the formulas sin(alpha + beta)= sin(alpha)cos(beta) + cos(alpha)sin(beta) and cos(alpha + beta)= cos(alpha)cos(beta) - sin(alpha)sin(beta). In 10-2 you have the tangent formula tan(alpha + beta)= tan(alpha) + tan(beta)/1-tan(alpha)tan(beta). Then there's 10-3.

10-3 Formulas

Doouble Formulas

Sin 2(alpha)= 2sin(alpha)cos(alpha)

Cos2(alpha)= cos^2(alpha)-sin^2(alpha) or 1-2sin^2(alpha) or 2cos^2(alpha)-1

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

Half Formulas

sin alpha/2=+/- the square root of 1-cos(alpha)/2

cos alpha/2= +/- the square root of 1+ cos(alpha)/2

tan alpha/2 = +/- the square root of 1-cos(alpha)/1+cos(alpha) or sin(alpha)/1+cos(alpha) or

1-cos(alpha)/sin(alpha)

Ex. Simplify 2sin(90 degrees)cos(90 degrees)

1) Sin2(90 degrees)

2)sin 180 degrees

3= 180-180= sin(0)

4)=0