Question 1169011
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:


<img src = "http://theo.x10hosting.com/2020/110406.jpg" >


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