This is related to my previous https://www.physicsforums.com/showthread.php?t=398964". I am having trouble to get the maximum of the following trigonometric function:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\cos^m\theta_1(c\cos^n\theta_2+s\sin^n\theta_2)+\sin^m\theta_1 ( c\sin^n\theta_2+s\cos^n\theta_2)

[/tex]

Here [tex]m,n\ge2 \mbox{ are fixed positive integers and } c,s[/tex] are fixed positive reals with [tex]c^2+s^2=1[/tex]. The maximum is to be carried out w.r.t. [tex]\theta_1,\theta_2[/tex] in the range [tex]0\le\theta_1,\theta_2\le\frac{\pi}{2}[/tex] In my trying, I got the maximum to be max(c,s), but I fear may be I have done some mistake. I got the result by differentiating w.r.t. [tex]\theta_1,\theta_2[/tex] and vanishing them....but I have ignored the case when [tex]\cos\theta_1\cos\theta_2\sin\theta_1\sin\theta_2\ne0[/tex]. Can anybody help me, please.

Can I say that the function is all time differentiable within its closed and compact domain (the rectangle), the maximum should be attained on boundary?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Maximum of a trigonometric function

**Physics Forums | Science Articles, Homework Help, Discussion**