Chapter 9

Write each expression in terms of its co-function. $$\sin \frac{1}{2}$$

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. $$-159^{\circ}$$

Use a calculator in radian mode to find approximations for cos \(s\) and sin s for each number s. Give as many decimal places as your calculator displays. (These are NOT exact values-they are only approximations.) Then determine the quadrant in which the point on the unit circle corresponding to s lies. Finally. find approximations for tan \(s\), cot \(s\), sec \(s\), and cse \(s\). $$0.75$$

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. $$y=1-\frac{2}{3} \sin \frac{3}{4} x$$

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

A ship travels 50 kilometers on a bearing of \(27^{\circ}\) and then travels on a bearing of \(117^{\circ}\) for 140 kilometers. Find the distance \(x\) between the starting point and the ending point.

Give the reference angle for each angle measure. $$98^{\circ}$$

Find the angle of least positive measure that is co terminal with the given angle. $$-40^{\circ}$$

Use a calculator in radian mode to find approximations for cos \(s\) and sin s for each number s. Give as many decimal places as your calculator displays. (These are NOT exact values-they are only approximations.) Then determine the quadrant in which the point on the unit circle corresponding to s lies. Finally. find approximations for tan \(s\), cot \(s\), sec \(s\), and cse \(s\). $$0.95$$

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. $$y=-1-2 \cos 5 x$$

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

Two ships leave a port at the same time. The first ship sails on a bearing of \(40^{\circ}\) at 18 knots (nautical miles per hour) and the second at a bearing of \(130^{\circ}\) at 26 knots. How far apart are they after 1.5 hours?

Give the reference angle for each angle measure. $$212^{\circ}$$

Find the angle of least positive measure that is co terminal with the given angle. $$-98^{\circ}$$

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. $$y=1-2 \cos \frac{1}{2} x$$

Graph each function over a one-period interval. $$y=\tan 4 x$$

Point \(A\) is 15.00 miles directly north of point \(B\). From point \(A\), point \(C\) is on a bearing of \(129^{\circ} 25^{\prime},\) and from point \(B\) the bearing of \(C\) is \(39^{\circ} 25^{\prime}\) (a) Find the distance between \(A\) and \(C\). (b) Find the distance between \(B\) and \(C\).

Give the reference angle for each angle measure. $$230^{\circ}$$

Begin by reproducing the graph in RiGuRE as. Keep in mind that for each of the four points labeled in the figure, \(r=1 .\) For each quadrantal angle, identify the appropriate values of \(x, y,\) and \(r\) to find the indicated function value. If it is undefined, say so. Check your answers with a calculator in degree mode. $$\text { sec } 180^{\circ}$$

Find the angle of least positive measure that is co terminal with the given angle. $$450^{\circ}$$

Use a calculator in radian mode to find approximations for cos \(s\) and sin s for each number s. Give as many decimal places as your calculator displays. (These are NOT exact values-they are only approximations.) Then determine the quadrant in which the point on the unit circle corresponding to s lies. Finally. find approximations for tan \(s\), cot \(s\), sec \(s\), and cse \(s\). $$-3.75$$

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. $$y=-3+3 \sin \frac{1}{2} x$$

Graph each function over a one-period interval. $$y=\tan \frac{1}{2} x$$

Point \(X\) is \(12.00 \mathrm{km}\) directly west of point \(Y\). From point \(X\), point \(Z\) is on a bearing of \(66^{\circ} 45^{\prime},\) and from point \(Y\) the bearing of \(Z\) is \(336^{\circ} 45^{\prime} .\) (a) Find the distance between \(X\) and \(Z\). (b) Find the distance between \(Z\) and \(Y\).

Give the reference angle for each angle measure. $$130^{\circ}$$

Begin by reproducing the graph in RiGuRE as. Keep in mind that for each of the four points labeled in the figure, \(r=1 .\) For each quadrantal angle, identify the appropriate values of \(x, y,\) and \(r\) to find the indicated function value. If it is undefined, say so. Check your answers with a calculator in degree mode. $$\csc 270^{\circ}$$

Find the angle of least positive measure that is co terminal with the given angle. $$539^{\circ}$$

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. $$y=-3+2 \sin \left(x+\frac{\pi}{2}\right)$$

Graph each function over a one-period interval. $$y=2 \tan x$$

Give the reference angle for each angle measure. $$-135^{\circ}$$

Find the angle of least positive measure that is co terminal with the given angle. $$-\frac{\pi}{4}$$

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. $$y=4-3 \cos (x-\pi)$$

Graph each function over a one-period interval. $$y=2 \cot x$$

Give the reference angle for each angle measure. $$-60^{\circ}$$

Find the angle of least positive measure that is co terminal with the given angle. $$-\frac{\pi}{3}$$

Use a calculator in radian mode to find approximations for cos \(s\) and sin s for each number s. Give as many decimal places as your calculator displays. (These are NOT exact values-they are only approximations.) Then determine the quadrant in which the point on the unit circle corresponding to s lies. Finally. find approximations for tan \(s\), cot \(s\), sec \(s\), and cse \(s\). $$5.5$$

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. $$y=\frac{1}{2}+\sin \left[2\left(x+\frac{\pi}{4}\right)\right]$$

Graph each function over a one-period interval. $$y=2 \tan \frac{1}{4} x$$

Give the reference angle for each angle measure. $$750^{\circ}$$

Begin by reproducing the graph in RiGuRE as. Keep in mind that for each of the four points labeled in the figure, \(r=1 .\) For each quadrantal angle, identify the appropriate values of \(x, y,\) and \(r\) to find the indicated function value. If it is undefined, say so. Check your answers with a calculator in degree mode. $$\text { cot } 540^{\circ}$$

Find the angle of least positive measure that is co terminal with the given angle. $$-\frac{3 \pi}{2}$$

Use a calculator in radian mode to find approximations for cos \(s\) and sin s for each number s. Give as many decimal places as your calculator displays. (These are NOT exact values-they are only approximations.) Then determine the quadrant in which the point on the unit circle corresponding to s lies. Finally. find approximations for tan \(s\), cot \(s\), sec \(s\), and cse \(s\). $$5.75$$

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. $$y=-\frac{5}{2}+\cos \left[3\left(x-\frac{\pi}{6}\right)\right]$$

Graph each function over a one-period interval. $$y=\frac{1}{2} \cot x$$

Give the reference angle for each angle measure. $$480^{\circ}$$

Find the angle of least positive measure that is co terminal with the given angle. $$-\pi$$

With your calculator in radian mode, work Exercises in order. Let \(s\) represent the number of letters in your first name. Find an approximation for \(\cos s\).

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. $$y=2 \sin (x-\pi)$$

Give the reference angle for each angle measure. $$\frac{4 \pi}{3}$$

Give an expression that generates all angles co terminal with each angle. Let n represent any integer. $$30^{\circ}$$