91Ó°ÊÓ

An equation of the terminal side of an angle \(\theta\) in standard position is given with a restriction on \(x\). Sketch the least positive such angle \(\theta,\) and find the val. ues of the six trigonometric functions of \(\theta\) . $$\sqrt{3} x+y=0, x \leq 0$$

Solve each problem involving an angle of elevation or depression. The length of the shadow of a building \(34.09 \mathrm{m}\) tall is \(37.62 \mathrm{m}\). Find the angle of elevation of the sun to the nearest hundredth of a degree.

Work each problem. In these exercises, assume the course of a plane or ship is on the indicated bearing. Two lighthouses are located on a north-south line. From lighthouse \(A\), the bearing of a ship 3742 m away is \(129^{\circ} 43^{\prime}\). From lighthouse \(B\), the bearing of the ship is \(39^{\circ} 43^{\prime}\). Find the distance between the lighthouses.

Work each problem. In these exercises, assume the course of a plane or ship is on the indicated bearing. The bearing from Winston-Salem, North Carolina, to Danville, Virginia, is \(N 42^{\circ}\) E. The bearing from Danville to Goldsboro, North Carolina, is \(S 48^{\circ}\) E. A car driven by Ellen Winchell, traveling at 65 mph, takes \(1.1 \mathrm{hr}\) to go from Winston-Salem to Danville and \(1.8 \mathrm{hr}\) to go from Danville to Goldsboro. Find the distance from Winston-Salem to Goldsboro.

A scanner antenna is on top of the center of a house. The angle of elevation from a point \(28.0 \mathrm{m}\) from the center of the house to the top of the antenna is \(27^{\circ} 10^{\prime},\) and the angle of elevation to the bottom of the antenna is \(18^{\circ} 10^{\prime} .\) Find the height of the antenna.

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. $$\sin \theta, \text { given that } \csc \theta=\frac{\sqrt{8}}{2}$$

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. $$\sin \theta, \text { given that } \csc \theta=1.42716321$$

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. $$74^{\circ}$$

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. $$218^{\circ}$$

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. $$178^{\circ}$$