Question

The point (-3/5,y) in the third quadrant corresponds to angle θ on the unit circle.

Answer 1

Sec(theta) = 1 / cos (theta) = hypotenuse / x -coordinate

hypotenuse = 1 (because it is the radius of the unit circle)

sec (theta) = 1 / (-3/5) = - 5/3

cot (theta) = 1 / tan(theta) = x-coordinate / y - coordinate

cot (theta) = -3/5 / y

y^2 + (-3/5)^2 = 1 => y^2 = 1 - 9/25 = 16/25 = y = +/- 4/5

Third quadrant => y = -4/5

=> cot (theta) = (-3/5) / (-4/5) = 3/4