10-3

This week I am going to teach you all how to work out trig problems by using formulas for sin 2a, cos 2a, tan 2a, sin a/2, cos a/2, and tan a/2. There are ten different formulas that we use for these types of problems. They are as follows:
• sin 2a= (2 sin a) (cos a)
• cos 2a= (cos^2 a) – (sin^2 a)
• cos 2a= 1- 2 sin^2 a
• cos 2a= 2 cos^2 a -1
• tan 2a= ( 2 tan a) / ( 1- tan^2 a)
• sin a/2= +/- sq. root of ((1 – cos a) / (2))
• cos a/2= +/- sq. root of (( 1+ cos a) / (2))
• tan a/2= +/- sq. root of (( 1- cos a) / ( 1+cos a))
• tan a/2= +/- (( sin a) / ( 1+ cos a))
• tan a/2= +/- (( 1- cos a) / (sin a))

Example:
Simplify cos^2 15 degrees – sin^2 15 degrees
• cos 2(15 degrees)
• cos 30 degrees
• (sq. root of 3) / (2)

-Braxton