Finding the horizontal tan() lines of this equation

[user02103498]

Homework Statement

Find all points on the graph of the function f(x)=2sinx+sin(^2)x,0≤x<2π at which the tangent line is horizontal. Please list the x-values below separating them with commas.

Relevant Equations

2sinx+sin(^2)x

I've been able to find the tangent line with most equations, but I don't have any idea how to do it with a range of values instead of being given a singular value.

 

[Joshy]

Hey, I think you're suppose to try to attempt a solution and show your work.

If the problem did not give you a range of values, then how would you try to solve this problem or what do you think you will see? Can you try a few of the first steps :)

 

[Office_Shredder]

Maybe a good starting point - can you describe what condition must be true for the tangent line to be horizontal?

 

[pasmith]

It may help to note $$2\sin x + \sin^2 x \equiv (1 + \sin x)^2 - 1.$$