cos2β if sinβ = 4/5 and β is in the first quadrant

Im having a hard time undersatanding this.

2 answers

recall your double-angle formula
cos2β = 1 - 2sin^2β = 1 - 2(4/5)^2 = 1 - 2*16/25 = -7/25
This makes sense, since β > π/4, so 2β > π/2, in QII

You will do well to do lots of these problems, to make sure you know the double-angle formulas by heart. They come up all the time.
Thank you very very much!!