Determine whether each statement is possible or impossible. See Example 4. cot θ = ―6

Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find csc θ , given that cot θ = ―1/2 and θ is in quadrant IV.

Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find cot θ , given that csc θ = ―1.45 and θ is in quadrant III.

If θ is an acute angle and cos θ = 1/3, find csc (𝜋/2 - θ).

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.

sin θ = √5/7 , and θ is in quadrant I.

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.

sin θ = √2/6 , and cos θ < 0

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.

csc θ = ―3 , and cos θ > 0

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.

cos θ = 1