sin2tsint4cost2 for t Solve the equation sin 2t sin t 4 co

sin2t+sint+4cost=-2 for t

Solve the equation sin 2t + sin t + 4 cos t = -2 for t. T [0, 2 pi) pi/3, 5 pi phi 2 pi/3 2 pi/3, 4 pi/3

Solution

sin2t+sint +4cost =-2

2sintcost+sint +4cost =-2

2sintcost+sint +4cost +2=0

sint(2cost+ 1) +2(2cost +1)=0

(2cost+ 1) (sint +2)=0

(2cost+ 1) =0

cost =-1/2

t =2pi/3 ,4pi/3