write it this way:
sin (2x) + √3 cosx = 0
2sinxcosx + √3cosx = 0
cosx(2sinx + √3) = 0
sinx = 0 or sinx = - √3/2
if sinx = 0
x = 0, π, 2π, ... ------> kπ , where k is an integer
if sinx = -√3/2
I know that sin30° = sin π/6 = +√3/2 , but x is in quadrants III or IV
so x = 180+30 = 210° = 7π/6
or x = 360-30 = 330° = 11π/6
the period of sinx is 2π
general :
x = 7π/6 + 2πk
x = 11π/6 + 2πl
x = 2πk
find the general solution for the equation:
sin2x+ square root 3cosx =0
1 answer