Double Angle

This past week in class we learned how to do the double- angle formula. I find this hard so I got my sister to help me with the homework and I am finally getting the hang of it. :)

Here are the Formulas we used in class:

Double-Angle Formulas:

sin2(alpha)=2sin(alpha)cos(alpha)

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

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

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

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

Half-Angle Formulas:

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

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

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

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

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

These formulas can be used for all of the problems throughout section 10-3.

Ex.1: Simplify:

2sin(60)cos(60)

sin2(60)=sin(120)

Ex.2: Simplify:

1-cos(20)/ sin(20)

tan(20)/2=tan(10)

Ex.3: Simplify:

2cos^2(20)-1

cos2(20)= cos40

=4 square root of 5

These are 3 examples that will be used throughout section 10-3.

Hope you had a great weekend, because I sure did. :)