Question

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

Answer 1

`-(2√(5) )/(5)`

Explanation:

The exact trigonometric value of cot theta = - sqrt5/2, pi/2 < theta < pi, tan theta is - 2sqrt5/5

Answer 2

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