any chance of solving for theta_g?

**rainer** · September 21st 2009, 11:36 AM

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

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

**Opalg** · September 21st 2009, 11:43 PM

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 $\cos^2\theta_\gamma$ .

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