Find the exact value of csc theta if cot theta = -2 and the terminal side of theta lies in quadrant II.

Answer 1

Given that cot theta = -2, we can rewrite this as:

cot theta = adjacent side / opposite side = -2

Let's assume adjacent side = -2x and opposite side = x. This assumption is made because the terminal side of theta lies in quadrant II, where x and -2x are both negative.

From the Pythagorean theorem, we have:

(-2x)^2 + x^2 = r^2
4x^2 + x^2 = r^2
5x^2 = r^2
r = x√5

Now, we can find the value of csc theta:

csc theta = hypotenuse / opposite side
csc theta = r / x
csc theta = x√5 / x
csc theta = √5

Therefore, csc theta = √5.