Let (5, -6) be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, tanθ

Question

Exact values please (fraction form if applicable, etc.). Thank you

Answer 1

I'm assuming that θ is from the x-axis to the line connecting the origin to (5, -6). You have a right triangle with sides 5 and -6, so the hypotenuse is √(5² + (-6)²) = √61. Then, using SOHCAHTOA, we have that

(1) cos(θ) = 5/√61

We also know that sin(θ) = -6/√61, which gives us

(2) csc(θ) = 1/sin(θ) = -√61/6

(3) tan(θ) = sin(θ)/cos(θ) = (5/√61)/(-6/√61) = -5/6