Question1he point $A(-40,-9)$ lies on the terminal arm of an angle in standard position. Determine the exact expression for he six trigonometric ratios of the angle.

Studdy Solution
Determine the cosecant, secant, and cotangent ratios:
Cosecant: $$\csc \theta = \frac{1}{\sin \theta} = \frac{41}{-9} = -\frac{41}{9}$$
Secant: $$\sec \theta = \frac{1}{\cos \theta} = \frac{41}{-40} = -\frac{41}{40}$$
Cotangent: $$\cot \theta = \frac{1}{\tan \theta} = \frac{40}{9}$$
The exact expressions for the six trigonometric ratios are:
$$\sin \theta = -\frac{9}{41}, \quad \cos \theta = -\frac{40}{41}, \quad \tan \theta = \frac{9}{40}$$
$$\csc \theta = -\frac{41}{9}, \quad \sec \theta = -\frac{41}{40}, \quad \cot \theta = \frac{40}{9}$$