2. Trigonometric Functions on Right Triangles

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Create a right triangle problem whose solution can be found by evaluating θ if sin θ = ¾.

In Exercises 61–62, use the figures shown to find the bearing from O to A.

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

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

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

Concept Check Suppose that ―90° < θ < 90° . Find the sign of each function value.

sec(―θ)

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