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 $\displaystyle \sin{2x} = \sin{(x - 4)}$ then $\displaystyle 2x = x - 4$ in the domain $\displaystyle 0<x<5$.

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 $\displaystyle \sin A = \sin B$, then $\displaystyle A = n\pi + (-1)^nB$

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

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

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

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

... and so on.

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

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