Question

How many solutions does the equation sin(4x)= 3/4?

Answer 1

`sin(4x)= (3)/(4)`


`4x=sin^-^1( (3)/(4)), \pi -sin^-^1( (3)/(4))`

Since sin is a periodic function, add the periodicity.


`4x=2\pi n+sin^-^1 ( (3)/(4) ) ,nEZ`


`4x=2\pi n-sin^-^1 ( (3)/(4) ) ,nEZ`


`x= (2\pi n+sin^-^1 ( (3)/(4) ) )/(4), nEZ`


`x= (2\pi n+ \pi -sin^-^1 ( (3)/(4) ) )/(4), nEZ`