# Thread: Intersection - Solve Trig Equation

1. ## Intersection - Solve Trig Equation

Hi, in order to integrate this function between 0 and pi/6 I need to solve for the intersection points to find the limits of integration. However, I am totally lost on how to solve it.

6cos(3x)-6sin(6x)=0

Any help would be kindly appreciated.

2. ## Re: Intersection - Solve Trig Equation

Originally Posted by sjmiller
Hi, in order to integrate this function between 0 and 6 I need to solve forthe intersection points to find the limits of integration. However, I amtotally lost on how to solve it.

6cos(3x)-6sin(6x)=0

Any help would be kindly appreciated.

The equation simplifies to cos(3x) - sin(6x) = 0.

There are several options for solving this. One option - depending on your background - is to use the double angle formula sin(6x) = 2 sin(3x) cos(3x), substitute, factorise, use the null factor law, solve for x.

3. ## Re: Intersection - Solve Trig Equation

Originally Posted by sjmiller
Hi, in order to integrate this function between 0 and 6 I need to solve forthe intersection points to find the limits of integration. However, I amtotally lost on how to solve it.

6cos(3x)-6sin(6x)=0

Any help would be kindly appreciated.

start by dividing by 6 ...

$\displaystyle \cos(3x) - sin(6x) = 0$

let $\displaystyle t = 3x$ ...

$\displaystyle \cos(t) - \sin(2t) = 0$

$\displaystyle \cos(t) - 2\sin(t)\cos(t) = 0$

$\displaystyle \cos(t)[1 - 2\sin(t)] = 0$

$\displaystyle \cos(t) = 0$ ... $\displaystyle \cos(3x) = 0$

$\displaystyle \sin(t) = \frac{1}{2}$ ... $\displaystyle \sin(3x) = \frac{1}{2}$

finish it ...

4. ## Re: Intersection - Solve Trig Equation

Hi, so it appears the answers are 1 and pi/6. But if this is the true set of solutions then how can the two functions intersect between 0 and pi/6 radians?

I know this is a bit off topic but perhaps it will help you understand what i'm trying to get at.

I need to find the area between the curves y=6cos(3x) and y=6sin(6x), x=0, x=pi/6... Does the compression factor 3 and 6 have an effect on their intersection in the given interval?

I get the period has been compressed by these factors but I'm not sure how to go about finding the solution in that interval...

5. ## Re: Intersection - Solve Trig Equation

Originally Posted by sjmiller
Hi, so it appears the answers are 1 and pi/6. But if this is the true set of solutions then how can the two functions intersect between 0 and pi/6 radians?

I know this is a bit off topic but perhaps it will help you understand what i'm trying to get at.

I need to find the area between the curves y=6cos(3x) and y=6sin(6x), x=0, x=pi/6... Does the compression factor 3 and 6 have an effect on their intersection in the given interval?

I get the period has been compressed by these factors but I'm not sure how to go about finding the solution in that interval...
this is what happens when one does not post the entire problem ...

the graphs cross at $\displaystyle x = \frac{\pi}{18}$ and $\displaystyle x = \frac{\pi}{6}$ ... I'll leave it for you to figure out why and which curve is above the other in the intervals $\displaystyle \left[0,\frac{\pi}{18}\right]$ and $\displaystyle \left[\frac{\pi}{18} , \frac{\pi}{6}\right]$

6. ## Re: Intersection - Solve Trig Equation

Thanks a lot for the help... Do you know of any good texts I can buy to decrease my lack of knowledge with trig functions. Were beginning trig integrals and I feel its going to end badly if I dont increase my knowledge.

Thanks.

7. ## Re: Intersection - Solve Trig Equation

you don't need a text ... go search on google. you'll find a veritable plethora of info on trig graphs and solving equations.

8. ## Re: Intersection - Solve Trig Equation

Originally Posted by skeeter
you don't need a text ... go search on google. you'll find a veritable plethora of info on trig graphs and solving equations.
The OP will also find a lot of info