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