# Area Between Two Curves (Sin and Cos)

1. Jan 22, 2012

### Jet1045

1. The problem statement, all variables and given/known data
Sketch the regions enclosed by the given curves. And determine the area between the curves.
y = 7 cos 3x, y = 7 sin 6x, x = 0, x = π/6

2. Relevant equations

3. The attempt at a solution

Okay so i ended up solving the question, because i used the help of my graphing calculator. To get the area between the two curves you need the intersection point between the two curves so that you can determine the limits of integration for the two integrals. However, i have no idea how you solve for the intersection point of those two trigonometric functions by hand. Maybe its really easy, and i am just having a dumb moment, but i needed to use my calculator to get it and of course you cant use calculators in university calc classes (or at least in mine). Someone pleaseee explain how to do this by hand if you can :)

2. Jan 22, 2012

### SammyS

Staff Emeritus
(My spell checker said that you spelled 'please' incorrectly.)
Can you give the equation you would use to solve for the point of intersection?

3. Jan 22, 2012

### Curious3141

To find the intersection point, set 7cos3x = 7sin6x, or simply cos3x = sin6x, since the sevens cancel out.

Then observe that sin6x = sin(2*3x), and use the double-angle formula for sine. Can you go from here?

4. Jan 23, 2012

### Jet1045

OHH i didnt know it would be that complicated, i thought you could just set them equal to eachother and there would be something obvious that i was just missing. K i will look up the double angle formula cause i have totally forgotten that stuff from high school. Thanks though :)

5. Jan 23, 2012

### Curious3141

Now put θ=3x.

6. Jan 23, 2012