Double Angle Formulas

Double Angle Formulas

Cos 2α=cos²α-sin²α                                Sin 2α = 2 sinα cosα

1.       Simplify  2 sin 10˚ cos 10˚

First you have to recognize this as the double angle formula for sin.

Then you multiply the given angle by 2.  So 10 times 2 is 20

The final simplified answer is sin 20˚

2.       Simplify  cos²15˚ - sin²15˚

First you recognize this as the double angle formula for cos

Then you multiply the given angle by 2.  So 15 times 2 is 30

That gives you cos 30˚=√3/2

3.       Find sin 2A and cos 2A if sin A= 5/13.

First you find cos A.  y=5, r=13, using Pythagorean thm you get that x=12.  So that means that cosA = 12/13

a.       Sin 2A = 2sinAcosA

=2(5/13)(12/13)

=120/169

b.      Cos 2A = cos²A-sin²A

=(12/13)²-(5/13)²

= (144/169) – (25/169)

= 119/169

Jenna Roussel