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# Trig question help ! watch

1. 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
2. (Original post by coconut64)
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
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 (everything else is outside the given domain)

Now do the same with the cos. It's slightly trickier with the values, but the process is the same.
3. Alternatively you could solve 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. (Original post by notnek)
Alternatively you could solve 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
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
5. (Original post by ghostwalker)
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.
6. (Original post by coconut64)
Thanks I managed to get it now.
Note: I've amended my previous post, as the 2pi solution is outside the given domain and so not valid.
7. (Original post by coconut64)
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
If you want to have a go then I recommend you watch the solution to 5c here.

That video shows how you can solve

which is similar to your problem.

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