Question

How do I find the general solution in a question when the coefficient of x is not one.
Eg. sin(3x)=1
cos(x/2)=2
etc. ?
Thanks!

Answer 1

sin(3x)=1
arcsin(sin(3x))=arcsin(1)
3x=arcsin(1)
3x=pi/2 + 2pi*n

Answer 2

where \(n \in \mathbb{Z} \)

Answer 3

there's an infinite number of solutions, as the sine is continuous, so it hits the 1 a lot of times. That's why the n