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I am having a problem understanding how to find a certain maximum of this equation and am not sure if I am going about this the proper way.

[tex] v^x_s = \frac{v \sin{\theta}}{1-v \cos{\theta}} [/tex]

Find an expression for the angle [tex] \theta_{max} [/tex] at which [tex] v^x_s [/tex] has its maximum value for a given speed v. Show that this angle satisfies the equation [tex] \cos{\theta_{max}}=v [/tex].

Answer: Using my knowledge of calculus, I believe I should take the derivative of the above equation with respect to [tex] \theta [/tex]

Using the quotient rule, this gives me [tex] \frac{v \cos{\theta}-v^2 (\sin{\theta})^2}{1-v \cos{\theta}} [/tex]

I should now find values of theta that make the equation 0 or undefined. However, I do not know what v is, which is throwing me off on what value theta should be. Any help would be greatly appreciated.

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# Finding the Maximum

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