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)

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )

6e14 is the answer.