1. ## Roots

((cosx)^2)(1+3(sinx)^2)=1

How do I find the root 54.7?

2. 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...

3. Do what Mathelogician says, giving you an equation in $[sin(x)]^2$, then substitute $u=[sin(x)]^2$ which gives you a quadratic in $u$, solve that then ...

CB

4. I think I have done it now. I did not get a quadratic equation. I got 2x^2-3x^4=0. I take out the factor 2x^2 and then 1-(3/2)x^2=0 gives the solutions other than 0, 180 and 360.

5. Is it generally preferable to let u=(sin x)^2 or let u=sin x?

6. Originally Posted by Stuck Man
Is it generally preferable to let u=(sin x)^2 or let u=sin x?
They are equivalent if you are careful about sines, but if the right hand side had been something other than 1 you would have ended up with the equivalent of u=(sin(x))^2 to get a quadratic.

7. Yes it's not quadratic and may seem a bit complicated.
Try this:
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