Chapter 6

The inverse sine, inverse cosine, and inverse tangent functions have the followings domains and ranges. (a) The function \(\sin ^{-1}\) has domain ________ and range _________ (b) The function \(\cos ^{-1}\) has domain ________ and range ________ (c) The function \(\tan ^{-1}\) has domain ________ and range _________

If the angle \(\theta\) is in standard position and \(P(x, y)\) is a point on the terminal side of \(\theta,\) and \(r\) is the distance from the origin to \(P,\) then \(\sin \theta=\) \(\frac{\square}{\square}\) \(\cos \theta=\) \(\frac{\square}{\square}\) \(\tan \theta=\) \(\frac{\square}{\square}\)

In which of the following cases must the Law of Cosines be used to solve a triangle? $$\begin{array}{llll}{\underline{\phantom{xx}}} & {\text { ASA }} & {\text { SSS }} & {\text { SAS }} & {\text { SSA }}\end{array}$$

In which of the following cases can we use the Law of Sines to solve a triangle? $$ \mathrm{ASA} \quad \mathrm{SSS} \quad \mathrm{SAS} \quad \mathrm{SSA} $$

The sign of a trigonometric function of \(\theta\) depends on the _____ in which the terminal side of the angle \(\theta\) lies. In Quadrant II, \(\sin \theta\) is _____ (positive/negative). In Quadrant III, \(\cos \theta\) is _____ (positive/negative). In Quadrant IV, \(\sin \theta\) is _____ (positive/negative).

The reciprocal identities state that \(\csc \theta=\) \(\frac{1}{\square}\) \(\sec \theta=\) \(\frac{1}{\square}\) \(\cot \theta=\) \(\frac{1}{\square}\)

Find the exact value of each expression, if it is defined. \(\begin{array}{lll}{\text { (a) } \sin ^{-1} \frac{1}{2}} & {\text { (b) } \cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)} & {\text { (c) } \tan ^{-1}(-1)}\end{array}\)

Find the reference angle for the given angle. $$ \begin{array}{llll}{\text { (a) } 150^{\circ}} & {\text { (b) } 330^{\circ}} & {\text { (c) }-30^{\circ}}\end{array} $$

Find the radian measure of the angle with the given degree measure. $$ 72^{\circ} $$

Find the exact value of each expression, if it is defined. (a) \(\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right) \quad\) (b) \(\cos ^{-1}\left(-\frac{\sqrt{2}}{2}\right) \quad\) (c) \(\tan ^{-1}(-\sqrt{3})\)

Find the reference angle for the given angle. $$ \begin{array}{llll}{\text { (a) } 120^{\circ}} & {\text { (b) }-210^{\circ}} & {\text { (c) } 780^{\circ}}\end{array} $$

Find the radian measure of the angle with the given degree measure. $$ 54^{\circ} $$

Find the exact value of each expression, if it is defined. \(\begin{array}{llll}{\text { (a) } \sin ^{-1}\left(-\frac{1}{2}\right)} & {\text { (b) } \cos ^{-1} \frac{1}{2}} & {\text { (c) } \tan ^{-1}\left(\frac{\sqrt{3}}{3}\right)}\end{array}\)

Find the reference angle for the given angle. $$ \begin{array}{llll}{\text { (a) } 225^{\circ}} & {\text { (b) } 810^{\circ}} & {\text { (c) }-105^{\circ}}\end{array} $$

Find the radian measure of the angle with the given degree measure. $$ -45^{\circ} $$

Find the exact value of each expression, if it is defined. \(\begin{array}{llll}{\text { (a) } \sin ^{-1}(-1)} & {} & {\text { (b) } \cos ^{-1} 1} & {} & {\text { (c) } \tan ^{-1} 0}\end{array}\)

Find the reference angle for the given angle. $$ \begin{array}{llll}{\text { (a) } 99^{\circ}} & {\text { (b) }-199^{\circ}} & {\text { (c) } 359^{\circ}}\end{array} $$

Find the radian measure of the angle with the given degree measure. $$ -60^{\circ} $$

Use a calculator to find an approximate value of each expression rounded to five decimal places, if it is defined. $$ \sin ^{-1}(0.45) $$

Find the reference angle for the given angle. $$ \begin{array}{llll}{\text { (a) } \frac{11 \pi}{4}} & {\text { (b) }-\frac{11 \pi}{6}} & {\text { (c) } \frac{11 \pi}{3}}\end{array} $$

Find the radian measure of the angle with the given degree measure. $$ -75^{\circ} $$

Use a calculator to find an approximate value of each expression rounded to five decimal places, if it is defined.. $$ \cos ^{-1}(-0.75) $$

Find the reference angle for the given angle. $$ \begin{array}{llll}{\text { (a) } \frac{4 \pi}{3}} & {\text { (b) } \frac{33 \pi}{4}} & {\text { (c) }-\frac{23 \pi}{6}}\end{array} $$

Find the radian measure of the angle with the given degree measure. $$ -300^{\circ} $$

Use a calculator to find an approximate value of each expression rounded to five decimal places, if it is defined. $$ \cos ^{-1}\left(-\frac{1}{4}\right) $$

Find the reference angle for the given angle. $$ \begin{array}{llll}{\text { (a) } \frac{5 \pi}{7}} & {\text { (b) }-1.4 \pi} & {\text { (c) } 1.4}\end{array} $$

Find the radian measure of the angle with the given degree measure. $$ 1080^{\circ} $$

Use a calculator to find an approximate value of each expression rounded to five decimal places, if it is defined. $$ \sin ^{-1} \frac{1}{3} $$

Find the reference angle for the given angle. $$ \begin{array}{llll}{\text { (a) } 2.3 \pi} & {\text { (b) } 2.3} & {\text { (c) }-10 \pi}\end{array} $$

Find the radian measure of the angle with the given degree measure. $$ 3960^{\circ} $$

Use a calculator to find an approximate value of each expression rounded to five decimal places, if it is defined. $$ \tan ^{-1} 3 $$

Find the exact value of the trigonometric function. $$ \sin 150^{\circ} $$

Find the radian measure of the angle with the given degree measure. $$ 96^{\circ} $$

Use a calculator to find an approximate value of each expression rounded to five decimal places, if it is defined. $$ \tan ^{-1}(-4) $$

Find the exact value of the trigonometric function. $$ \sin 225^{\circ} $$

Find the radian measure of the angle with the given degree measure. $$ 15^{\circ} $$

Solve triangle \(A B C\). \(a=3.0, \quad b=4.0, \quad \angle C=53^{\circ}\)

13-18 $$ Sketch each triangle, and then solve the triangle using the Law of Sines. $$ \angle A=50^{\circ}, \quad \angle B=68^{\circ}, \quad c=230 $$

Find the exact value of the trigonometric function. $$ \cos 210^{\circ} $$

Find the radian measure of the angle with the given degree measure. $$ 7.5^{\circ} $$

Use a calculator to find an approximate value of each expression rounded to five decimal places, if it is defined. $$ \sin ^{-1}(-2) $$

Solve triangle \(A B C\). \(b=60, \quad c=30, \quad \angle A=70^{\circ}\)

13-18 $$ Sketch each triangle, and then solve the triangle using the Law of Sines. $$ \angle A=23^{\circ}, \quad \angle B=110^{\circ}, \quad c=50 $$

Find the exact value of the trigonometric function. $$ \cos \left(-60^{\circ}\right) $$

Find the radian measure of the angle with the given degree measure. $$ 202.5^{\circ} $$

Solve triangle \(A B C\). \(a=20, \quad b=25, \quad c=22\)

13-18 $$ Sketch each triangle, and then solve the triangle using the Law of Sines. $$ \angle A=30^{\circ}, \quad \angle C=65^{\circ}, \quad b=10 $$

Find the exact value of the trigonometric function. $$ \tan \left(-60^{\circ}\right) $$

Find the degree measure of the angle with the given radian measure. $$ \frac{7 \pi}{6} $$

Solve triangle \(A B C\). \(a=10, \quad b=12, \quad c=16\)