Maximizing Triangle Area with Calculus

[tachu101]

Homework Statement

The vertices of a triangle are (0,0), (x, cos x), and (sin3x, 0), where 0 < x < p/2.
a. If A(x) represents the area of the triangle, write a formula for A(x).
b. Find the value of x for which A(x) is a maximum. Justify your answer.
c. What is the maximum area of the triangle?

Homework Equations

I know this involves min/max problems, and the area of a triangle at some point.

The Attempt at a Solution

No idea where to start. I don't see any way to get an area function for the triangle.

 

[HallsofIvy]

You do know that the area of a triangle if "1/2 base times height", don't you? Draw a picture and see what base and height are for this triangle.

 

[tachu101]

So is A(x)= (1/2)(sinx)^3(cosx)? If that's true then do I have to take the derivative or something?

 

[Tedjn]

Is it sin3x or (sinx)^3? Once that is cleared up, how would you usually find the maximum of a function? A derivative would help.