Chapter 9

Write each expression in terms of its co-function. $$\sin 38^{\circ}$$

An equation of the terminal side of an angle \(\theta\) in standard position is given with a restriction on \(x\). Sketch the least positive angle \(\theta\), and find the values of the six trigonometric functions of \(\theta\). $$-6 x-y=0, x \leq 0$$

Convert each angle measure to degrees, minutes, and seconds. Use a calculator as necessary. Round to the nearest second. $$31.4296^{\circ}$$

Graph each function over a two-period interval. State the phase shift. $$y=3 \sin \left(x-\frac{3 \pi}{2}\right)$$

Graph each function over a one-period interval. $$y=\csc \left(x+\frac{\pi}{3}\right)$$

A hump-back whale researcher is watching a whale approach directly toward her as she observes from the top of a lighthouse. When she first begins watching, the angle of depression of the whale is \(15^{\circ} 50^{\prime} .\) Just as the whale turns away from the lighthouse, the angle of depression is \(35^{\circ} 40^{\prime} .\) If the height of the lighthouse is 68.7 meters, find the horizontal distance \(x\) traveled by the whale as it approaches the lighthouse.

Write each expression in terms of its co-function. $$\cos 19^{\circ}$$

An equation of the terminal side of an angle \(\theta\) in standard position is given with a restriction on \(x\). Sketch the least positive angle \(\theta\), and find the values of the six trigonometric functions of \(\theta\). $$-5 x-3 y=0, x \leq 0$$

Convert each angle measure to degrees, minutes, and seconds. Use a calculator as necessary. Round to the nearest second. $$59.0854^{\circ}$$

Graph each function over a two-period interval. State the phase shift. $$y=2 \cos (x+\pi)$$

Graph each function over a one-period interval. $$y=\sec \left(\frac{1}{2} x+\frac{\pi}{3}\right)$$

An antenna is on top of the center of a house. From a point on the ground 28.0 meters from the center of the house, the angle of elevation 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.

Write each expression in terms of its co-function. $$\tan 25^{\circ} 43^{\prime}$$

An equation of the terminal side of an angle \(\theta\) in standard position is given with a restriction on \(x\). Sketch the least positive angle \(\theta\), and find the values of the six trigonometric functions of \(\theta\). $$-4 x+7 y=0, x \leq 0$$

Convert each angle measure to degrees, minutes, and seconds. Use a calculator as necessary. Round to the nearest second. $$89.9004^{\circ}$$

Graph each function over a two-period interval. State the phase shift. $$y=-5 \sin \left(x+\frac{\pi}{2}\right)$$

Graph each function over a one-period interval. $$y=\csc \left(\frac{1}{2} x-\frac{\pi}{4}\right)$$

The angle of elevation from Lone Pine to the top of Mt. Whitney is \(10^{\circ} 50^{\prime} .\) A driver, traveling 7.00 kilometers from Lone Pine along a straight, level road toward Mt. Whitney, finds the angle of elevation to be \(22^{\circ} 40^{\prime} .\) Find the height of the top of Mt. Whitney above the level of the road.

Write each expression in terms of its co-function. $$\sin 38^{\circ} 29^{\prime}$$

An equation of the terminal side of an angle \(\theta\) in standard position is given with a restriction on \(x\). Sketch the least positive angle \(\theta\), and find the values of the six trigonometric functions of \(\theta\). $$6 x-5 y=0, x \geq 0$$

Convert each angle measure to degrees, minutes, and seconds. Use a calculator as necessary. Round to the nearest second. $$102.3771^{\circ}$$

Refer to Example \(4 .\) Do not use a calculator. Let s correspond to the point ( \(x, y\) ) on the unit circle. (a) Determine the quadrant where ( \(x, y\) ) is located. (b) Determine whether sin \(s\) and cos \(s\) are positive or negative. $$s=-\frac{3 \pi}{4}$$

Graph each function over a two-period interval. State the phase shift. $$y=\sin \left(2 x+\frac{\pi}{4}\right)$$

Graph each function over a one-period interval. $$y=2+3 \sec (2 x-\pi)$$

Write each expression in terms of its co-function. $$\cos \frac{\pi}{5}$$

An equation of the terminal side of an angle \(\theta\) in standard position is given with a restriction on \(x\). Sketch the least positive angle \(\theta\), and find the values of the six trigonometric functions of \(\theta\). $$x+y=0, x \geq 0$$

Sketch each angle in standard position. Draw an arrow representing the correct amount of notation. Find the measure of two other angles, one positive and one negative, that are co terminal with the given angle. Give the quadrant of each angle. $$75^{\circ}$$

Let \(s\) correspond to the point \((x, y)\) on the unit circle. \(s=\frac{\pi}{7}\) (a) Determine the quadrant where \((x, y)\) is located. (b) Determine whether sin \(s\) and \(\cos s\) are positive or negative.

Graph each function over a two-period interval. State the phase shift. $$y=\cos \left(3 x-\frac{3 \pi}{5}\right)$$

Graph each function over a one-period interval. $$y=1-2 \csc \left(x+\frac{\pi}{2}\right)$$

Write each expression in terms of its co-function. $$\sin \frac{\pi}{3}$$

An equation of the terminal side of an angle \(\theta\) in standard position is given with a restriction on \(x\). Sketch the least positive angle \(\theta\), and find the values of the six trigonometric functions of \(\theta\). $$x-y=0, x \geq 0$$

Sketch each angle in standard position. Draw an arrow representing the correct amount of notation. Find the measure of two other angles, one positive and one negative, that are co terminal with the given angle. Give the quadrant of each angle. $$89^{\circ}$$

Find the (a) amplitude, (b) period, (c) phase shift (if any). (d) vertical translation (if any), and (e) range of each finction. Then graph the function over at least one period. $$y=-4 \sin (2 x-\pi)$$

Graph each function over a one-period interval. $$y=1-\frac{1}{2} \csc \left(x-\frac{3 \pi}{4}\right)$$

A ship leaves port and sails on a bearing of \(\mathrm{N} 28^{\circ} 10^{\prime} \mathrm{E}\). Another ship leaves the same port at the same time and sails on a bearing of \(\mathrm{S} 61^{\circ} 50^{\prime} \mathrm{E} .\) If the first ship sails at \(24.0 \mathrm{mph}\) and the second sails at \(28.0 \mathrm{mph}\), find the distance \(x\) between the two ships after 4 hours.

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

Sketch each angle in standard position. Draw an arrow representing the correct amount of notation. Find the measure of two other angles, one positive and one negative, that are co terminal with the given angle. Give the quadrant of each angle. $$174^{\circ}$$

Find the (a) amplitude, (b) period, (c) phase shift (if any). (d) vertical translation (if any), and (e) range of each finction. Then graph the function over at least one period. $$y=3 \cos (4 x+\pi)$$

Graph each function over a one-period interval. $$y=2+\frac{1}{4} \sec \left(\frac{1}{2} x-\pi\right)$$

Radio direction finders are set up at two points \(A\) and \(B\), which are 2.50 miles apart on an east-west line. From \(A\), it is found that the bearing of a signal from a radio transmitter is \(\mathrm{N} 36^{\circ} 20^{\prime} \mathrm{E}\). and the bearing of the same signal from \(B\) is \(N 53^{\circ} 40^{\prime} \mathrm{W}\) Find the distance of the transmitter from \(B\).

Write each expression in terms of its co-function. $$\csc 0.3$$

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

Sketch each angle in standard position. Draw an arrow representing the correct amount of notation. Find the measure of two other angles, one positive and one negative, that are co terminal with the given angle. Give the quadrant of each angle. $$234^{\circ}$$

Find the (a) amplitude, (b) period, (c) phase shift (if any). (d) vertical translation (if any), and (e) range of each finction. Then graph the function over at least one period. $$y=\frac{1}{2} \cos \left(\frac{1}{2} x-\frac{\pi}{4}\right)$$

Graph each function over a one-period interval. $$y=\tan x$$

Sketch each angle in standard position. Draw an arrow representing the correct amount of notation. Find the measure of two other angles, one positive and one negative, that are co terminal with the given angle. Give the quadrant of each angle. $$-61^{\circ}$$

Find the (a) amplitude, (b) period, (c) phase shift (if any). (d) vertical translation (if any), and (e) range of each finction. Then graph the function over at least one period. $$y=-\frac{1}{4} \sin \left(\frac{3}{4} x+\frac{\pi}{8}\right)$$

Graph each function over a one-period interval. $$y=\cot x$$

A plane flies 1.5 hours at 110 mph on a bearing of \(40^{\circ} .\) It then turns and flies 1.3 hours at the same speed on a bearing of \(130^{\circ} .\) How far is the plane from its starting point?