6sin^2x - 5sinx-4=0 [-7 пи /2 ; -3 пи/2]

Question

6sin^2x - 5sinx-4=0 [-7 пи /2 ; -3 пи/2]

Answer 1

Sinx=a
6a²-5a-4=0
D=25+96=121
a1=(5-11)/12=-1/2⇒sinx=-1/2
x=-π/6+2πn
-7π/2≤-π/6+2πn≤-3π/2
-21≤-1+12n≤-9
-20≤12n≤-8
-5/3≤n≤-2/3
n=-1  x=-π/6-2π=-13π/6
a2=(5+11)/12=4/3⇒sinx=4/3>1 нет решения