Answer:
3π/2<x<2π
Step-by-step explanation:
What is the answer to this question?
Given the expression
2sinx + 3 > sin²x
Rearrange
sin²x-2sinx - 3>0
Let P = sinx
P²-2P-3>3
Factorize
P²-3P+P-3>0
P(P-3)+1(P-3)>0
(P-3)(P+1)>0
P-3>0 and P+1>0
P>3 and P>-1
Substitute P = sinx
Sinx>3 and sinx>-1
x > sin^-1 3 and x > sin^-1 (-1)
x>-90°
Since sin is negative in the 3rd and 4th quadrant
x>270+90
x>360 or x>2π
In the 4th quadrant
x>360-90
x > 270
x > 3π/2
Combine the inequalities
3π/2<x<2π
