Finding Intersection Point Between Two Trigonometric Functions

[doctordiddy]

Homework Statement

Find the area of the region enclosed between y=4sin(x) and y=3cos(x) from x=0 to x=0.3π.

Homework Equations

The Attempt at a Solution

So I know how to do most of this question, the area i am stuck on is finding the intersection point between the two functions, since i know you must have two different areas and then add them to find the total area.

I am looking to find this intersection point without a calculator.

I tried to equate 4sinx=3cosx, changing this to 3/4=sinx/cosx, then tanx=3/4. This gets me nowhere though, can anyone help?

 

[Dick]

Homework Statement

Find the area of the region enclosed between y=4sin(x) and y=3cos(x) from x=0 to x=0.3π.

Homework Equations

The Attempt at a Solution

So I know how to do most of this question, the area i am stuck on is finding the intersection point between the two functions, since i know you must have two different areas and then add them to find the total area.

I am looking to find this intersection point without a calculator.

I tried to equate 4sinx=3cosx, changing this to 3/4=sinx/cosx, then tanx=3/4. This gets me nowhere though, can anyone help?

I'm not sure why you are trying to pull this off without a calculator, but if tan(x)=3/4 then x=arctan(3/4). So you've found the intersection. The integral from 0 to arctan(3/4) actually comes out pretty neatly. Doing the integral from arctan(3/4) to 3*pi/10 can also be done if you are ok with things like cos(3*pi/10) and sin(3*pi/10) appearing in the final answer. At that point I'd use a calculator if you want an actual number.