# Thread: Calc II - Area btw curves

1. ## Calc II - Area btw curves

Hi, I have an area between curves problem that I am stuck on and I think it is because I need to use a double-angle identity in my figuring of my intersection points, but I don't know how to to this when I have coefficients that are greater than 2.
Here is the problem:

Find the area between the following curves:
y=7cos(4x), y=7sin(8x) x=o x= pi/8

I am trying to find where the first two intersect:
7cos(4x) = 7sin(8x)

7cos(4x) - 7sin(8x) = 0 *I factored out the 7. Should I reduce the 4x to x and the 8x to 2x and then use the double angle identity for sin2x?

I keep getting my intersection as pi/2, which is not in the domain of the area limited by these curves.
Any help is greatly appreciated! Thanks!
Molly

2. $7\cos(4x) - 7\sin(8x) = 0$

$7\cos(4x) - 14\sin(4x)\cos(4x) = 0$

$7\cos(4x)[1 - 2\sin(4x)] = 0$

$\cos(4x) = 0$ ... $x = \frac{\pi}{8}$

$\sin(4x) = \frac{1}{2}$ ... $x = \frac{\pi}{24}$

$A = 7 \int_{\frac{\pi}{24}}^{\frac{\pi}{8}} \sin(8x) - \cos(4x) \, dx$

3. Thank you so much!!