So my company is paying for me to finish up my mechanical engineering degree so I'm taking Calc in night school. Now I'm stuck and have to turn in this take home quiz tonight and I'm stuck on what should be a pretty easy one. Some of you fresh college students, give me a hand:

So here's the problem:
[img]http://www.stonehousebrewery.com/~dsyring/calctroubles.JPG[/img]

I'm supposed to solve for the value of a that gives me the largest area shown in red. Good bad or otherwise, I've gotten to a point where my derivative looks to be

2(cos(a) - a sin(a))

and I set that equal to 0 to find my max and get stuck with

a sin(a) = cos(a)

Anybody remember how to do this? Am I on the right track? Help a brotha out! *:-)

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Pleasantly missing since 2006

You are a peice of something...I have plenty on Volume, but after looking through 5 old notebooks, nothing on area. Which branch of Calculus is this anyhow? I have slight experience in Intuitive Calculus and Analytic Geometry/Calculus II.

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You sir, are an idiot.

Just really basic Calc 1 stuff supposedly, though my teacher does have a history of giving us problems to do that he hasn't worked out himself, that turn out to be impossible. I'm thinking this isn't one of them though. We've done problems similar to this in class before, but never with trig values. That's where I get hung up everytime. Anyways, anybody else have a clue?

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Pleasantly missing since 2006

uh.... a = cot(a) so where does a equal it's cotangent?

I solved it for you.

The area of that red box will be A=w*h (width times height).

The width of the red box is from -a to +a, or 2a.

The height of the box at a is cos(a).

So, the area of the box is A=(2a)cos(a).

We want to find the maximum area, the maximum A, so use the product rule take the derivative of that function.

A' = [2cos(a)] + [(2a)(-sin(a))]

The maximum A will be where it's slop is 0, where A' = 0.

It will be approximately 0.860.

That is your maximum area, so plug that into the first equation.

0.860 = (2a)cos(a)

Solve for a.

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Hey thanks for the efforts guys. Anyways, I'm in class now and the same old thing happened. He hadn't taught us enough to solve the problem properly, so all he wanted us to do was to put the diferential function in our graphing calculators and just give a decimal approximation. Stupid. Sorry I bothered everyone.

Thanks for the help though!

Oh, and Jurkyboy, that's what I got so kuddo's to you!

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Pleasantly missing since 2006