# Thread: any chance of solving for theta_g?

1. ## any chance of solving for theta_g?

Any chance of solving for $\theta_\gamma$?

$x=\sqrt{\frac{b^2\sin^2\theta_\gamma+\cos^2\theta_ \gamma}{\tan^2\theta_\gamma+1}}$

2. Originally Posted by rainer
Any chance of solving for $\theta_\gamma$?

$x=\sqrt{\frac{b^2\sin^2\theta_\gamma+\cos^2\theta_ \gamma}{\tan^2\theta_\gamma+1}}$
Start with the fact that $\tan^2\theta_\gamma+1 = \sec^2\theta_\gamma = 1/\cos^2\theta_\gamma$. So $x = \sqrt{(b^2\sin^2\theta_\gamma+\cos^2\theta_\gamma) \cos^2\theta_\gamma}$. Square both sides, replace $\sin^2\theta_\gamma$ by $1-\cos^2\theta_\gamma$, and you have a quadratic equation for $\cos^2\theta_\gamma$.