Question

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

Answer 1

$sin(4x)= \dfrac{3}{4}$ 

$4x=sin^-^1( \dfrac{3}{4}), \pi -sin^-^1( \dfrac{3}{4})$ 

Since sin is a periodic function, add the periodicity. 

$4x=2\pi n+sin^-^1 ( \dfrac{3}{4} ) ,nEZ$ 

$4x=2\pi n-sin^-^1 ( \dfrac{3}{4} ) ,nEZ$ 

$x= \dfrac{2\pi n+sin^-^1 ( \dfrac{3}{4} ) }{4}, nEZ$ 

$x= \dfrac{2\pi n+ \pi -sin^-^1 ( \dfrac{3}{4} ) }{4}, nEZ$