If cot θ = -√3 then how do you find the exact value of theta in QII without using the calculator

find cot θ" = √3 first

cot θ" = √3
tan θ" = 1/√3

this is an exact triangle, with sides 1 and √3 and hypotenuse of 2
recall the angle required for this triangle

θ" = 30 degrees

but tan θ negative
on the unit circle, tan θ is negative in the 2nd and 4th quadrants which correspond to θ = 180 - θ" and θ = 360 - θ" respectively

θ = 180 - 30
= 150 degrees
θ = 360 - 30
= 330 degrees

these are the two solutions

cot = x / y
in Q2, x is negative and y is positve, so
x = -sqrt(3) and y = 1

we also know that x^2 + y^2 = r^2
(-sqrt(3))^2 + 1^2 = 3 + 1 = 4 = r^2
r = 2 (always positive)

this defines a 30-60-90 triangle, since the ratio of the sides is 1:sqrt(3):2
since the short side is opposite the 30 degree angle, that means it makes the 30 degree angle with the x-axis

180 - 30 = 150

theta = 150 or 5pi/6

you need to know your special angles! (multiples of 30,45, and 60)

first of all there is no minus value for cot theta.
cot theta is equal to adjacent side over opposite side
in your case adj side = 1.7321 & opp side = 1
therefore angle is 30 deg
(it should be plus & not minus)

You have a 1, 2, sqrt(3) triangle in Q2
θ = 180 - 30 = 150 degrees

Don't you just hate Calc lol