How many solutions does the equation sin(4x)=1/2 have on the interval (0,2pi)?

2 solutions

Step-by-step 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)

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x