How do you use a double angle identity to find the exact value of each expression?

1 Answer
Mar 6, 2015

You would need an expression to work with.

For example:
Given #sinalpha=3/5# and #cosalpha=-4/5#, you could find #sin2 alpha# by using the double angle identity
#sin2 alpha=2sin alpha cos alpha#.

#sin2 alpha=2(3/5)(-4/5)=-24/25#.

You could find #cos2 alpha# by using any of:
#cos2 alpha=cos^2 alpha -sin^2 alpha#
#cos2 alpha=1 -2sin^2 alpha#
#cos2 alpha=2cos^2 alpha -1#

In any case, you get #cos alpha=7/25#.