# Math Help - Trigonometry

1. ## Trigonometry

Find all the angles, in terms of pi, for 0<x<5 which satisfy the equation
sin2x=sin(x-4)

2. Originally Posted by acc100jt
Find all the angles, in terms of pi, for 0<x<5 which satisfy the equation
sin2x=sin(x-4)
If $\sin{2x} = \sin{(x - 4)}$ then $2x = x - 4$ in the domain $0.

Surely you can solve that...

3. ## Trig equations

Hello acc100jt
Originally Posted by acc100jt
Find all the angles, in terms of pi, for 0<x<5 which satisfy the equation
sin2x=sin(x-4)
In general, if $\sin A = \sin B$, then $A = n\pi + (-1)^nB$

For example, when $n=0, A =B$

When $n = 1, A = \pi - B$

When $n = 2, A = 2\pi + B$

When $n = -1, A = -\pi - B$

... and so on.

So, what you have to do is to solve the equation $2x = n\pi +(-1)^n(x-4)$ for all the values of $n$ that give values of $x$ in the required range.

So try the values of $n$ that I've given above: $0, 1, 2, -1,$ ...etc and see what happens.