If cos θ = 2/3 and 270° < θ < 360° then determine the exact value of 1/cot

Answer 1

Q4. cosA = 2/3 = X/r,

X^2 + Y^2 = r^2,
2^2 + Y^2 = 3^2,
4 + Y^2 = 9,
Y^2 = 9 - 4 = 5,
Y = +-sqrt5,
Y = -sqrt5(Q4).

1/cotA = tanA = Y/X = -(sqrt5/2).