# Thread: A quick explaination

1. ## A quick explaination

hi guys,

I dont know if this is in the right forum because it involves trig stuff. So mod, feel free to move it.

i was just going through some work on the topic 'area between two curves' and i was given the equations as:

f(x) = sin x, and g(x) = sin(2x), a = 0 and b = 'pi'

The solution states that the intersection point could be found as:

sin x = sin(2x), then x = 'pi' - 2x and hence x = 'pi'/3.

i was wondering could someone show me how the step by step as to how they derived the intersection point? Because i never did trig before

2. Hi

$\displaystyle sin (2x) = 2 sin (x) cos (x)$ and in the problem $\displaystyle sin (2x) = sin (x)$. If $\displaystyle x \neq 2\pi k, k \in \mathbb{Z}$, then $\displaystyle 2 cos (x) = 1$ thus $\displaystyle x = \frac {\pi}{3}$

3. Thanks.

If its not too much trouble could you explain a lil bit further please?

4. Originally Posted by Redeemer_Pie
Thanks.

If its not too much trouble could you explain a lil bit further please?
No problem, just translation of the math language:

We know that $\displaystyle sin (2x) = 2 sin (x) cos (x)$. Your problem states that $\displaystyle sin (2x) = sin (x)$, so $\displaystyle 2 sin (x) cos (x) = sin (x)$. Now, if $\displaystyle sin (x) \neq 0$ we can divide by it and $\displaystyle 2 cos (x) = 1$ => $\displaystyle x = \frac{1}{3} \pi$

5. Thanks mate