# Proving the greatest value for Tan

• Dec 8th 2008, 04:52 AM
thepopasmurf
Proving the greatest value for Tan
I'm revising for an exam and I'm stuck on part of my revision question.
I have proven that $\displaystyle Tan\theta=\frac{5sin\alpha}{13-5cos\alpha}$ in the given question, but now I have to prove that $\displaystyle tan\theta$ has the greatest value at $\displaystyle cos\alpha=\frac{5}{13}$
Can anyone help me prove it?
• Dec 8th 2008, 04:56 AM
mr fantastic
Quote:

Originally Posted by thepopasmurf
I'm revising for an exam and I'm stuck on part of my revision question.
I have proven that $\displaystyle Tan\theta=\frac{5sin\alpha}{13-5cos\alpha}$ in the given question, but now I have to prove that $\displaystyle tan\theta$ has the greatest value at $\displaystyle cos\alpha=\frac{5}{13}$
Can anyone help me prove it?

Use calculus to find the maximum of $\displaystyle y = \frac{5sin\alpha}{13-5cos\alpha}$:

Solve $\displaystyle \frac{dy}{d \alpha} = 0$ etc.
• Dec 8th 2008, 05:02 AM
thepopasmurf
I thought about using calculus but I'm fairly sure it can be done without it. The book stays away from calculus until differential equations
• Dec 8th 2008, 10:45 AM
thepopasmurf
I'm sorry, but does anyone have any ideas?