Question

Let (-3, 8) be a point on the terminal side of Theta.

Find the exact values of sin theta , csc theta, and cot theta.

Answer 1

When we have a given point (x, y) in rectangular coordinates, the angle between the x-axis and a line that connects the origin with that point is given by:

Tan(θ) = y/x

In this case the point is (-3, 8)

Then we have:

Tan(θ) = -8/3

θ = Atg(-8/3) = -69.4°

Now we just need to input this on:

Sin(-69.4°) = -0.94

Csc(-69.4°) = 1/Sin(-69.4°) = 1/-0.94 = -1.1

Cot(-69.4°) = 1/tan(-69.4°) = -3/8 = -0.38