SOLUTION: Please help me Solve this equation on [0,360) sin^3 (x) = sin(x) Thank you in advance

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Question 1169011: Please help me Solve this equation on [0,360)
sin^3 (x) = sin(x)
Thank you in advance
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your original equation is:

sin^3(x) = sin(x)

divide both side of the equation by sin(x) to get:

sin^2(x) = 1

take the square root of both sides of the equation to get:

sin(x) = plus or minus sqrt(1).

since sqrt(1) is equal to 1, this becomes;

sin(x) = plus or minus 1.

when sin(x) = 1, solve for x to get:

x = arcsin(1) = 90 degrees.

when sin(x) = -1, solve for x to get:

x = arcsin(-1) = -90 degrees.

what you want is the equivalent angle that is greater than 0 and less then 360 degrees.

add 360 to -90 and you get 270 degrees.

that's the angle you're looking for.

arcsin(-1) = 270 degrees.

i believe your answer will be x = 90 and 270 degrees.

the equation of sin^3(x) - sin(x) can be graphed.

to graph it, set up 4 equations.

they will be:

y = sin^3(x)
y = sin(x)
y = 1
y = -1

the intersection of these 4 equations will be your solution.

the graph looks like this:

note that sin^3(x) is equivalent to sin(x)^3.

Answer by greenestamps(13209) (Show Source):
You can put this solution on YOUR website!

Consider this a polynomial equation with "sin(x)" as the variable. Then solve it like any other polynomial equation: get everything on one side of the equation set equal to 0 and factor.

or or

On the interval [0,360) the solutions are 0 and 180 (sin(x)=0), 90 (sin(x) = 1), and 270 (sin(x) = -1).

ANSWERS: 0, 90, 180, and 270