1. ## Maximization

This may not even count as a calculus question, simply because I've already done the calculus part. I just don't know how to do the algebra to solve it haha. So if this needs to be moved, I apologize.

Anyway! Here is the problem and what I've done:

Problem: An electric current, I, in amps, is given by $\displaystyle I = cos(Ct) + sqrt(3)sin(Ct)$ where C /= 0 is a constant. Find the minimum and maximum values of I. For what values of t will these occur if $\displaystyle 0 <= t <= 2pi$.

My work:
I know how to find the max and min values. I took the derivative, set it to 0, and began solving for t.

$\displaystyle \frac{dI}{dt} = \sqrt{3}C cos(Ct) - Csin(Ct)$

$\displaystyle 0 = \sqrt{3} C cos(Ct) - Csin(Ct)$

Factored out a c and got:

$\displaystyle 0 = \sqrt{3}cos(Ct) - sin(Ct)$

So...how do I solve for t from this point? Do I use the arccosine and arcsine? I'm not sure...I just can't seem to remember how to do it!

Thanks for any help!

2. Quote:
"

Factored out a c and got:

"

Sin(Ct)=root3 Cos(Ct)

now square both sides

sin^2(Ct)=3Cos(Ct)

pythagorean identity

1-cos^2(Ct)=3Cos(Ct)

get on one side

cos^2(Ct)+3Cos(Ct)-1=0

use quadratic formula to find cos(Ct)
one of the answers is -3.3ish which isn't possible
for cos and the other is .30277 which is possible for cos
so use that one.