2. Trigonometric Functions on Right Triangles

Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3. csc θ > 0 , cot θ > 0

Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3. tan θ < 0 , cot θ < 0

Solve each problem. Height of a Lunar Peak The lunar mountain peak Huygens has a height of 21,000 ft. The shadow of Huygens on a photograph was 2.8 mm, while the nearby mountain Bradley had a shadow of 1.8 mm on the same photograph. Calculate the height of Bradley. (Data from Webb, T., Celestial Objects for Common Telescopes, Dover Publications.)

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.)Length of Sides of an Isosceles Triangle An isosceles triangle has a base of length 49.28 m. The angle opposite the base is 58.746°. Find the length of each of the two equal sides.

Determine whether each statement is possible or impossible. See Example 4. tan θ = 0.93

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.)Find a formula for h in terms of k, A, and B. Assume A < B.

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