What are the solutions of the equation 2sin(4x)=1 on the interval [0,π)?
2sin (4x) = 1 divide both sides by 2
sin (4x) = 1/2
Note that sin (x) = 1/2 at pi/6, 5pi/6, 13pi/6, 17pi/6
Dividing these angles by 4 gives us the solutions
x = pi/24 , 5pi/24, 13 pi/24 , 17 pi /24