2. Trigonometric Functions on Right Triangles

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. tan θ = ―15/8 , and θ is in quadrant II .

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. cos θ = 1

Concept CheckSuppose that 90° < θ < 180° .Find the sign of each function value. tan θ/2

Concept CheckSuppose that 90° < θ < 180° .Find the sign of each function value. cot (θ + 180°)

Concept CheckSuppose that ―90° < θ < 90° .Find the sign of each function value. sec θ/2

Concept CheckSuppose that ―90° < θ < 90° .Find the sign of each function value. sec(―θ)

Concept CheckSuppose that ―90° < θ < 90° .Find the sign of each function value. cos(θ―180°)

Concept Check Find a solution for each equation. tan (3θ ― 4°) = 1 / [cot(5θ ― 8°)]

Concept Check Find a solution for each equation. sin(4θ + 2°) csc(3θ + 5°) = 1

Concept Check Find a solution for each equation. sec(2θ + 6°) cos(5θ + 3°) = 1