How do I find the root 54.7?
What do you mean by the root 54.7?
You can use the identity sinx^2+cosx^2=1 to converte sine into cosine or cosine into sine form and then solve the quadratic eqution. Just check your final solutions because of the equation's beeing in quadratic form...
Yes it's not quadratic and may seem a bit complicated.
To avoid confusion let sinx = a and cosx = b and sin(2x)=c
so we have b^2+3(ab)^2=1 => 3(ab)^2=1-b^2=a^2 => (3/4)c^2 = a^2 =>
(3/4)c^2 - a^2 = 0 => (sqrt3/2 c - a)(sqrt3/2 c + a)=0
Then solve each expression; Just in solving each one, remember that sin(2x)=2sinx.cosx