Absolute Max/Min of a Trig Function

[Sczisnad]

I am having some issues with going about finding the max and min of trig functions over a set interval. Normally with finding the max and min of a function over an interval the first thing that I do is find the derivative of that function, Then i set the derivative to 0 and solve to find the critical points. Now this is where I run into problems...

Ex. Find the Max/Min values of f on the interval [0,pi/2] f(t)=2cos(t)+sin(2t)My work:

f(t)=2cos(t)+sin(2t) "the original function"

f'(t)=2cos(2t)-2sin(t) "I found it's derivative"

0=2cos(2t)-2sin(t) "finding where f' is equal to 0"

0=cos(2t)-sin(t) "simplified"

But now what? With a normal function you get a nice x=?,?,? ...

SO how can i find the critical values for a trig function and how can I then find the Max and Min over a set interval?

 

[fzero]

You can use trig identities to rewrite $$\cos(2t)$$ entirely in terms of $$\sin^2t$$. This will leave you with a quadratic equation in terms of $$\sin t$$ to solve.

 

[micromass]

So you need to solve cos(2t)-sin(t)=0. Is suggest you first use the formula cos(2t)=1-2sin²(t). Then you have a quadratic equation in sin(t) which can be solved with the usual methods...