If sint 23 and t Is in quadrant II find cost sect csct tant

If sin(t) = 2/3, and t Is in quadrant II, find cos(t), sec(t), csc(t), tan(t), cot(t). cos(t) = Squareroot 5/3 csc(t) = 3/2 sec(t) = 3/Squareroot 5 tan(t) = Squareroot 5/2 cot(t) = 2/Squareroot 5

Solution

sint = 2/3 ; t is in QII

cost = sqrt(1 -sin^2t) = sqrt(1 - 4/9) = - sqrt5/3     ( cos is -ve in Q-II)

csc(t) = 1/sint = 3/2

sect = 1/cosy = =3/sqrt5

tant = sint/cost = 2/3 / -sqrt5/3 = -2/sqrt5

cot(t) = 1/tant = -sqrt(5)/2