Trig question help !

how do I solve for sin4x-sin3x=0 for 0<x<pi? I don't get how the formula sin p- sinq can be used because cos 3.5x will be created... I don't know what to do with the 3.5x ...

Thanks

Alternatively you could solve $\sin4\theta = \sin 3\theta$ by considering the sine graph / CAST.

This is quicker but can be confusing for a lot of students.

E.g. the first solution is when $4\theta = 3\theta$

You don't need to do anything with the 3.5x.


You have 2 cos 3.5x sin 0.5x = 0

so, cos 3.5x = 0 or sin 0.5x = 0

If sin 0.5x = 0, then 0.5x = 0, pi, 2pi, 3pi, etc.
Hence x = 0, 2pi, 4pi, 6pi, etc.
Now restrict it to the desired domain, x = 0, or 2pi.

Now do the same with the cos. It's slightly trickier with the values, but the process is the same.

Thanks I managed to get it now.

I don't think I had ever learnt that method to solve it. I do know the cast diagram but not the method but thanks