find:

Question

tanx=-3
one period and all angles

3csc^2x=4
one period and all angles

sin2x+cosx-0
one period

Answer 1

the first two are real easy, you should have no problems with them

the third:

sin 2x + cosx = 0
2sinxcosx + cosx = 0
cosx(2sinx + 1) = 0
cosx = 0 or sinx = -1/2

if cosx = 0 , x = π/2 or 3π/2
if sinx = =1/2) , x = 7π/6 or x = 11π/6