2. Trigonometric Functions on Right Triangles

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

Give all six trigonometric function values for each angle θ .Rationalize denominators when applicable. sec θ = ―√5 , and θ is in quadrant II

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

Determine whether each statement is possible or impossible. a. sec θ = ―2/3

Determine whether each statement is possible or impossible. b. tan θ = 1.4

Determine whether each statement is possible or impossible. c. cos θ = 5

Solve each problem. See Examples 3 and 4.The figure to the right indicates that the equation of a line passing through the point (a, 0) and making an angle θ with the x-axis is y = (tan θ) (x - a).Find an equation of the line passing through the point (5, 0) that makes an angle of 15° with the x-axis.