Question

решите неравенство 6*cos^2t+sint>4

Answer 1

6-6sin²t+sint-4>0
6sin²t-sint-2<0
sint=a
6a²-a-2<0
D=1+48=49
a1=(1-7)/12=-1/2
a2=(1+7)/12=2/3
-1/2<a<2/3⇒-1/2<sint<2/3
t∈(-π/6+2πn;arcsin2/3+2πn) U (π-arcsin2/3+2πn;7π/6+2πn)