Find, in terms of pi, the solutions of the equation sin5x + sin x = 0

[CathyLou]

Hi.

Could someone please help me with the following C3 question? I would really appreciate any help as I am completely stuck at the moment.

Find, in terms of pi, the solutions of the equation sin5x + sin x = 0 for x in the interval 0 >= x > pi.

I wrote down that sin(3x + 2x) + sin x = 0 and that sin3xcos2x + cos3xsin2x + sin x = 0 but I am not sure where to go from here or if this is even the correct method.

Thank you.

Cathy

 

[unplebeian]

You have to use the Sin C + sin D formula. If you don't know how to derive it add sin(x+y) and sin(x-y) together, call x+y= A and x-y= B, then solve for x and y and resubst to get:

sin A + sin B= 2sin ((A+B)/2) x cos ((A-B)/2)

That should help you.

Your interval is 0 >= x > p which reads as 0 is greater than x and x is greater than pi, so 0 is greater than pi?