The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.

Question

(5, −9)

sin (𝜃) =

cos (𝜃) =

tan (𝜃) =

csc (𝜃) =

sec (𝜃) =

cot (𝜃) =

Answer 1

The length of vector (5, -9) is

sqrt(5² + 9²) = sqrt(146)

By definition of the trigonometric functions

sin(θ) = -9/sqrt(146)

cos(θ) = 5/sqrt(146)

tan(θ) = -9/5

csc(θ) = -sqrt(146)/9

sec(θ) = sqrt(146)/5

cot(θ) = -5/9