Cot theta = - square root 5/2, pi/2 < theta < pi, tan theta find the exact trigonometric value

Cot (theta) = - square root 5/2 ... pi/2< theta < pi

This means that the angle theta is in the second quadrant and cos (theta) has a negative value.

cot (theta) = cos (theta) / sin (theta)

We can calculate the equivalent value of the angle in the first quadrant

Which is ... cot^ (-1) (sqrt (5/2)) = 32.31 degrees

And now, the exact trigonometric value is 180 - 32.31 = 147.69 degrees