BackSolve 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. See Example 2.
―15°
Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 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.
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.)