how do i solve sin(4x)=(√3)/2?

Question

how do i solve these types of questions? Can someone explain how to solve these types of questions because i have a test on this on monday

Answer 1

Think of it as solving

sin(y) = √3/2

But in our case, y = 4x.

Where is sine equal to √3/2? Presuming an interval restriction of
0 to 2pi, this is true at the points pi/3 and 2pi/3. Since there is no restriction given, we have to add 2k(pi) to each solution, and write it as

4x = { pi/3 + 2k(pi) | k an integer} U
{ 2pi/3 + 2k(pi) | k an integer }

Multiplying both sides by (1/4), we get

x = { pi/12 + k(pi/2) | k an integer) U {pi/6 + k(pi/2) | k an integer}

Answer 2

sin4x=(3)^1/2 /2
sin4x=sin(pi/3)
4x=n(pi)+(-1)^n * pi/3 n is integer
x=n(pi)/4+ (-1)^n * pi/12