Answer:
2 solutions
Explanation:
Given the equation sin(4x)=1/2, to know the total number of solutions that the equation has within the interval (0,2π), we will need to solve for x first.
sin(4x)=1/2
4x = arcsin1/2
4x = 30°
x = 30/4
x1 = 7.5° (This angle lies in the first quadrant)
Since sine is positive in the second quadrant as well and the angle in the second quadrant is (180°-theta) where theta is 7.5°, therefore;
x2 = 180-7.5°
x2 = 172.5°
Therefore 7.5° and 172.5° are the two solutions of x that falls within the range (0,2π)