Graph analysis with trig involved

[airportman92]

Homework Statement

given: y=sin2x-2sinx

Homework Equations

The Attempt at a Solution

i already found the roots of the equation, i also found the first and second derivatives which are 2cosx2-2cosx and -4sin2x+2sinx. however, i do not know how to find the roots for these equations in order to do mins and maxes and inflection pt. is it true that the inflection piont is zero, because that's how someone said to do it, but would that mean no concavity at all? and the original is differentiable and continuous correct? also, how wouuld i find the domain and range of this?

 

[rock.freak667]

For the first derivative, use the double angle formula

cos2x=2cos²x-1 = 1-2sin²x

Solve for x and sub that into the expression for y''.