how do you solve: find cos2x if sinx is equal to 1/5

1 answer

cos2x if sinx = 1/5
(1-2sin^2 x)(sinx) = 1/5
sinx - 2 sin^3 x = 1/5
5sinx - 10sin^3 x = 1
10sin^3 x - 5sinx + 1 = 0

Now you have a nasty cubic to solve
I use this on-line cubic equation solver
http://www.1728.com/cubic.htm

it gave me
sinx = .56959
sinx = -.79143
sinx = .22183

each of those will give you 2 different solutions

I will do the first
if sinx = .56959 , x is in quadrants I or II and
x = 34.72° or x = 145.28°

there will be 6 answers between 0 and 360