Chapter 6

For triangle \(A B C\) with sides \(a, b,\) and \(c\) the Law of Cosines states \(c^{2}=\) ________________________

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 \(\sin \theta=\text{_____}\) \(\cos \theta=\text{_____}\) \(\tan \theta=\text{_____}\)

In which of the following cases must the Law of cosines be used to solve a triangle? $$ASA\quad SSS\quad SAS\quad SSA$$

In which of the following cases can we use the Law of Sines to solve a triangle? ASA SSS SAS 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).

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

Find the reference angle for the given angle. (a) \(150^{\circ}\) (b) \(330^{\circ}\) (c) \(-30^{\circ}\)

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

Find the reference angle for the given angle. (a) \(120^{\circ}\) (b) \(-210^{\circ}\) (c) \(780^{\circ}\)

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

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. (a) \(\sin ^{-1}\left(-\frac{1}{2}\right)\) (b) \(\cos ^{-1} \frac{1}{2}\) (c) \(\tan ^{-1}\left(\frac{\sqrt{3}}{3}\right)\)

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

Find the reference angle for the given angle. (a) \(99^{\circ}\) (b) \(-199^{\circ}\) (c) \(359^{\circ}\)

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

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

Find the reference angle for the given angle. (a) \(\frac{11 \pi}{4}\) (b) \(-\frac{11 \pi}{6}\) (c) \(\frac{11 \pi}{3}\)

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

Find the reference angle for the given angle. (a) \(\frac{4 \pi}{3}\) (b) \(\frac{33 \pi}{4}\) (c) \(-\frac{23 \pi}{6}\)

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

Find the reference angle for the given angle. (a) \(\frac{5 \pi}{7}\) (b) \(-1.4 \pi\) (c) \(1.4\)

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

Find the reference angle for the given angle. (a) \(2.3 \pi\) (b) \(2.3\) (c) \(-10 \pi\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Find the exact value of the trigonometric function. $$\text { sec } 300^{\circ}$$