Solve the inequality sinx>square root x.

Answer 1

sin x > √x
we can say immediately that x≥0 , since we can't take the square root of a negative.
so I would graph y = sinx
and y = √x and look at the region where the sinx is above the √x

http://www.wolframalpha.com/input/?i=y+%3D+sin%28x%29+%2C+y+%3D+√x+for+x≥0

notice that they both pass though the origin, but after that they never intersect or touch again, and the sine is always above the square root function.

so x ≥ 0

Answer 2

mis-stated the result of the graph

notice that the sin(x) is always below y = √x
so there is no solution to
sin(x) > √x