SOLUTION: Solve the equation for solutions in the interval 0 ≤ x < 2𝜋. Round approximate solutions to the nearest ten-thousandth. 4 sin^3 x = sin x

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the equation for solutions in the interval 0 ≤ x < 2𝜋. Round approximate solutions to the nearest ten-thousandth. 4 sin^3 x = sin x      Log On


   

Question 1178160: Solve the equation for solutions in the interval 0 ≤ x < 2𝜋. Round approximate solutions to the nearest ten-thousandth.
4 sin^3 x = sin x
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
this is 4sin^3x-sin x=0
sin x(4 sin^2x-1)=0=sin x(2 sin x+1)(2 sin x-1)
x=0 degrees
x=30 and 150 degrees
x=210 and 330 degrees; graph in radians
graph%28300%2C300%2C-2%2C6%2C-1%2C2%2C4sin%28x%29%5E3%2Csin%28x%29%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

4sin%5E3+%28x%29+=+sin+%28x%29
4sin%5E3+%28x%29%2Fsin+%28x%29+=+sin+%28x%29%2Fsin+%28x%29
4sin%5E2+%28x%29+=+1
sin%5E2+%28x%29+=+1%2F4
sin%28x%29+=+sqrt%281%2F4%29
sin%28x%29+=+1%2F2 or sin%28x%29+=+-1%2F2
since given the interval+0+%3C=+x+%3C+2pi, go with positive solution sine is positive in quadrants I and II only
sin%28x%29+=+1%2F2
x=sin%5E-1%281%2F2%29
solutions in radians:
x=0
x=pi=+3.14159->rounded to the nearest ten-thousandth
x=7pi%2F6=+3.66519+
x=11pi%2F6=5.75959
x=pi%2F6=0.52360+
x=5pi%2F6=2.61799
solutions in degrees:
x=0°
x=180°
x=210°
x=330°
x=30°
x=150°