2. Trigonometric Functions on Right Triangles

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1. sin θ , given that csc θ = √24/3

Solve each problem. See Examples 1 and 2.Distance between Two Ships Two ships leave a port at the same time. The first ship sails on a bearing of 52° at 17 knots and the second on a bearing of 322° at 22 knots. How far apart are they after 2.5 hr?

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1. sin θ , given that csc θ = 1.25

Solve each problem. See Examples 1 and 2.Distance between Two Ships A ship leaves its home port and sails on a bearing of S 61°50'. Another ship leaves the same port at the same time and sails on a bearing of N 28°10'E. If the first ship sails at 24.0 mph and the second sails at 28.0 mph, find the distance between the two ships after 4 hr.

Concept Check What is wrong with the following item that appears on a trigonometry test? "Find sec θ , given that cos θ = 3/2 . "

Solve each problem. See Examples 1 and 2.Flying Distance The bearing from A to C is N 64° W. The bearing from A to B is S 82° W. The bearing from B to C is N 26° E. A plane flying at 350 mph takes 1.8 hr to go from A to B. Find the distance from B to C.

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. SeeExample 2. 84°

Solve each problem. See Examples 1 and 2.Distance between Two Cities The bearing from Atlanta to Macon is S 27° E, and the bearing from Macon to Augusta is N 63° E. An automobile traveling at 62 mph needs 1¼ hr to go from Atlanta to Macon and 1¾ hr to go from Macon to Augusta. Find the distance from Atlanta to Augusta.

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. SeeExample 2. 178°

Solve each problem. See Examples 3 and 4.Height of an Antenna A scanner antenna is on top of the center of a house. The angle of elevation from a point 28.0 m from the center of the house to the top of the antenna is 27°10', and the angle of elevation to the bottom of the antenna is 18°10'. Find the height of the antenna.

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. SeeExample 2. ―15°

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. SeeExample 2. ―345°

Solve each problem. See Examples 3 and 4.Distance through a Tunnel A tunnel is to be built from point A to point B. Both A and B are visible from C. If AC is 1.4923 mi and BC is 1.0837 mi, and if C is 90°, find the measures of angles A and B.

Give all six trigonometric function values for each angle θ .Rationalize denominators when applicable. cos θ = ―5/8 , and θ is in quadrant III

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