Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designed to be solved without a calculator. In Exercises 14, give the value of the angle \(\theta\) in degrees. \(\theta=-\frac{\pi}{6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designed to be solved without a calculator. In Exercises 14, give the value of the angle \(\theta\) in degrees. \(\theta=-\frac{5 \pi}{6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designed to be solved without a calculator. In Exercises 14, give the value of the angle \(\theta\) in degrees. \(\theta=\frac{25 \pi}{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designed to be solved without a calculator. In Exercises 14, give the value of the angle \(\theta\) in degrees. \(\theta=\frac{16 \pi}{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designed to be solved without a calculator. In Exercises 58, use special triangles to evaluate: \(\tan \frac{\pi}{6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designed to be solved without a calculator. In Exercises 58, use special triangles to evaluate: \(\cot \frac{\pi}{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designed to be solved without a calculator. In Exercises 58, use special triangles to evaluate: \(\csc \frac{\pi}{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designed to be solved without a calculator. In Exercises 58, use special triangles to evaluate: \(\sec \frac{\pi}{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designed to be solved without a calculator. In Exercises 9 and 10, use a right triangle to find the other five trigonometric functions of the acute angle \(\theta\). \(\sin \theta=\frac{5}{13}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designed to be solved without a calculator. In Exercises 9 and 10, use a right triangle to find the other five trigonometric functions of the acute angle \(\theta\). \(\cos \theta=\frac{15}{17}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, identify the one angle that is not coterminal with all the others. \(150^{\circ}, \ 510^{\circ},\ -210^{\circ}, \ 450^{\circ}, \ 870^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, identify the one angle that is not coterminal with all the others. \(\frac{5 \pi}{3},\ -\frac{5 \pi}{3}, \ \frac{11 \pi}{3},\ -\frac{7 \pi}{3}, \ \frac{365 \pi}{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 36, evaluate the six trigonometric functions of the angle \(\theta\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 36, evaluate the six trigonometric functions of the angle \(\theta\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 36, evaluate the six trigonometric functions of the angle \(\theta\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 36, evaluate the six trigonometric functions of the angle \(\theta\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, point P is on the terminal side of angle \(\theta\). Evaluate the six trigonometric functions for \(\theta\). If the function is undefined, write undefined. P(3, 4)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, point P is on the terminal side of angle \(\theta\). Evaluate the six trigonometric functions for \(\theta\). If the function is undefined, write undefined. P(-4, -6)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, point P is on the terminal side of angle \(\theta\). Evaluate the six trigonometric functions for \(\theta\). If the function is undefined, write undefined. P(0, 5)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, point P is on the terminal side of angle \(\theta\). Evaluate the six trigonometric functions for \(\theta\). If the function is undefined, write undefined. P(-3, 0)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, point P is on the terminal side of angle \(\theta\). Evaluate the six trigonometric functions for \(\theta\). If the function is undefined, write undefined. P(5, -2)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, point P is on the terminal side of angle \(\theta\). Evaluate the six trigonometric functions for \(\theta\). If the function is undefined, write undefined. P(22, -22)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, state the sign (+ or -) of (a) sin t, (b) cos t, and (c) tan t for values of t in the interval given. \(\left(0,\ \frac{\pi}{2}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, state the sign (+ or -) of (a) sin t, (b) cos t, and (c) tan t for values of t in the interval given. \(\left(\frac{\pi}{2},\ \pi\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, state the sign (+ or -) of (a) sin t, (b) cos t, and (c) tan t for values of t in the interval given. \(\left(\pi,\ \frac{3\pi}{2}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, state the sign (+ or -) of (a) sin t, (b) cos t, and (c) tan t for values of t in the interval given. \(\left(\frac{3\pi}{2},\ 2\pi\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, determine the sign (+ or -) of the given value without the use of a calculator. \(\cos 143^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, determine the sign (+ or -) of the given value without the use of a calculator. \(\tan 192^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, determine the sign (+ or -) of the given value without the use of a calculator. \(\cos \frac{7 \pi}{8}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, determine the sign (+ or -) of the given value without the use of a calculator. \(\tan \frac{4 \pi}{5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, choose the point on the terminal side of \(\theta\). \(\theta=45^{\circ}\) (a) (2, 2) (b) \((1,\ \sqrt{3})\) (c) \((\sqrt{3},\ 1)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, choose the point on the terminal side of \(\theta\). \(\theta=\frac{2 \pi}{3}\) (a) (-1, 1) (b) \((-1,\ \sqrt{3})\) (c) \((-\sqrt{3},\ 1)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, choose the point on the terminal side of \(\theta\). \(\theta=\frac{7 \pi}{6}\) (a) \((-\sqrt{3},\ -1)\) (b) \((-1,\ \sqrt{3})\) (c) \((-\sqrt{3},\ 1)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, choose the point on the terminal side of \(\theta\). \(\theta=-60^{\circ}\) (a) (-1, -1) (b) \((1,\ -\sqrt{3})\) (c) \((-\sqrt{3},\ 1)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\cos 120^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\tan 300^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\sec \frac{\pi}{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\csc \frac{3\pi}{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\sin \frac{13\pi}{6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\cos \frac{7\pi}{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\tan -\frac{15\pi}{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\cot \frac{13\pi}{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\cos \frac{23\pi}{6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\cos \frac{17\pi}{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\sin \frac{11\pi}{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2536, evaluate without using a calculator by using ratios in a reference triangle. \(\cot \frac{19\pi}{6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3742, find (a) \(\sin \theta\), (b) \(\cos \theta\), and (c) \(\tan \theta\) for the given quadrantal angle. If the value is undefined, write undefined. \(-450^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3742, find (a) \(\sin \theta\), (b) \(\cos \theta\), and (c) \(\tan \theta\) for the given quadrantal angle. If the value is undefined, write undefined. \(-270^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3742, find (a) \(\sin \theta\), (b) \(\cos \theta\), and (c) \(\tan \theta\) for the given quadrantal angle. If the value is undefined, write undefined. \(7 \pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3742, find (a) \(\sin \theta\), (b) \(\cos \theta\), and (c) \(\tan \theta\) for the given quadrantal angle. If the value is undefined, write undefined. \(\frac{11\pi}{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3742, find (a) \(\sin \theta\), (b) \(\cos \theta\), and (c) \(\tan \theta\) for the given quadrantal angle. If the value is undefined, write undefined. \(-\frac{7\pi}{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3742, find (a) \(\sin \theta\), (b) \(\cos \theta\), and (c) \(\tan \theta\) for the given quadrantal angle. If the value is undefined, write undefined. \(-4 \pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, evaluate without using a calculator. Find \(\sin \theta\) and \(\tan \theta\) if \(\cos \theta=\frac{2}{3}\) and \(\cot \theta>0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, evaluate without using a calculator. Find \(\cos \theta\) and \(\cot \theta\) if \(\sin \theta=\frac{1}{4}\) and \(\tan \theta<0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, evaluate without using a calculator. Find \(\tan \theta\) and \(\sec \theta\) if \(\sin \theta=-\frac{2}{5}\) and \(\cos \theta>0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, evaluate without using a calculator. Find \(\sin \theta\) and \(\cos \theta\) if \(\cot \theta=\frac{3}{7}\) and \(\sec \theta<0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, evaluate without using a calculator. Find \(\sec \theta\) and \(\csc \theta\) if \(\cot \theta=-\frac{4}{3}\) and \(\cos \theta<0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, evaluate without using a calculator. Find \(\csc \theta\) and \(\cot \theta\) if \(\tan \theta=-\frac{4}{3}\) and \(\sin \theta>0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, evaluate by using the period of the function. \(\sin \left(\frac{\pi}{6}+49,000 \pi\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, evaluate by using the period of the function. \(\tan (1,234,567 \pi)-\tan (7,654,321 \pi)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, evaluate by using the period of the function. \(\cos \left(\frac{5,555,555 \pi}{2}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, evaluate by using the period of the function. \(\tan \left(\frac{3 \pi-70,000 \pi}{2}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Use a calculator to evaluate the expressions in Exercises 4952. Does your calculator give the correct answers? Many calculators miss all four. Give a brief explanation of what probably goes wrong.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Give a convincing argument that the period of sin t is \(2\pi\). That is, show that there is no smaller positive real number p such that sin (t + p) = sin t for all real numbers t.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Refracted Light Light is refracted (bent) as it passes through glass. In the figure, \(\theta_{1}\) is the angle of incidence and \(\theta_{2}\) is the angle of refraction. The index of refraction is a constant \(\mu\) that satisfies the equation \(\sin \theta_{1}=\mu \sin \thet

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Refracted Light A certain piece of crown glass has an index of refraction of 1.52. If a light ray enters the glass at an angle \(\theta_{1}=42^{\circ}\), what is \(\sin \theta_{2}\)?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Damped Harmonic Motion A weight suspended from a spring is set into motion. Its displacement d from equilibrium is modeled by the equation \(d=0.4 e^{-0.2 t} \cos 4 t\), where d is the displacement in inches and t is the time in seconds. Find the displacement at the given time.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Swinging Pendulum The Columbus Museum of Science and Industry exhibits a Foucault pendulum 32 ft long that swings back and forth on a cable once in approximately 6 sec. The angle \(\theta\) (in radians) between the cable and an imaginary vertical line is modeled by the equation \(

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Too Close for Comfort An F-15 aircraft flying at an altitude of 8000 ft passes directly over a group of vacationers hiking at 7400 ft. If \(\theta\) is the angle of elevation from the hikers to the F-15, find the distance d from the group to the jet for the given angle. (a) \(\theta=45^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Manufacturing Swimwear Get Wet, Inc., manufactures swimwear, a seasonal product. The monthly sales x (in thousands) for Get Wet swimsuits are modeled by the equation \(x=72.4+61.7 \sin \frac{\pi t}{6}\), where t = 1 represents January, t = 2 February, and so on. Estimate the n

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False If \(\theta\) is an angle of a triangle such that \(\cos \theta<0\), then \(\theta\) is obtuse. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False If \(\theta\) is an angle in standard position determined by the point (8, -6), then \(\sin \theta=-0.6\). Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
You should answer these questions without using a calculator. Multiple Choice If \(\sin \theta=0.4\), then \(\sin (-\theta)+\csc \theta=\) (A) -0.15. (B) 0. (C) 0.15. (D) 0.65. (E) 2.1.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
You should answer these questions without using a calculator. Multiple Choice If \(\cos \theta=0.4\), then \(\cos (\theta+\pi)=\) (A) -0.6. (B) -0.4. (C) 0.4. (D) 0.6. (E) 3.54.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
You should answer these questions without using a calculator. Multiple Choice The range of the function \(f(t)=(\sin t)^{2}+(\cos t)^{2}\) is (A) {1}. (B) [-1, 1]. (C) [0, 1]. (D) [0, 2]. (E) \([0,\ \infty)\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
You should answer these questions without using a calculator. Multiple Choice If \(\cos \theta=-\frac{5}{13}\) and \(\tan \theta>0\), then \(\sin \theta=\) (A) \(-\frac{12}{13}\). (B) \(-\frac{5}{12}\). (C) \(\frac{5}{13}\). (D) \(\frac{5}{12}\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6770, find the value of the unique real number \(\theta\) between 0 and \(2\pi\) that satisfies the two given conditions. \(\sin \theta=\frac{1}{2}\) and \(\tan \theta<0\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6770, find the value of the unique real number \(\theta\) between 0 and \(2\pi\) that satisfies the two given conditions. \(\cos \theta=\frac{\sqrt{3}}{2}\) and \(\sin \theta<0\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6770, find the value of the unique real number \(\theta\) between 0 and \(2\pi\) that satisfies the two given conditions. \(\tan \theta=-1\) and \(\sin \theta<0\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6770, find the value of the unique real number \(\theta\) between 0 and \(2\pi\) that satisfies the two given conditions. \(\sin \theta=-\frac{\sqrt{2}}{2}\) and \(\tan \theta>0\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 7174 refer to the unit circle in this figure. Point P is on the terminal side of an angle t and point Q is on the terminal side of an angle \(t+\pi / 2\). Using Geometry in Trigonometry Drop perpendiculars from points P and Q to the x-axis to form two right triangles. Explain ho

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 7174 refer to the unit circle in this figure. Point P is on the terminal side of an angle t and point Q is on the terminal side of an angle \(t+\pi / 2\). Using Geometry in Trigonometry If the coordinates of point P are (a, b), explain why the coordinates of point Q are (-b, a).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 7174 refer to the unit circle in this figure. Point P is on the terminal side of an angle t and point Q is on the terminal side of an angle \(t+\pi / 2\). Explain why \(\sin \left(t+\frac{\pi}{2}\right)=\cos t\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 7174 refer to the unit circle in this figure. Point P is on the terminal side of an angle t and point Q is on the terminal side of an angle \(t+\pi / 2\). Explain why \(\cos \left(t+\frac{\pi}{2}\right)=-\sin t\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn In the figure for Exercises 7174, t is an angle with radian measure \(0<t<\pi / 2\). Draw a similar figure for an angle with radian measure \(\pi / 2<t<\pi\) and use it to explain why \(\sin (t+\pi / 2)=\cos t\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Use the accompanying figure to explain each of the following. (a) \(\sin (\pi-t)=\sin t\) (b) \(\cos (\pi-t)=-\cos t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Approximation and Error Analysis Use your grapher to complete the table to show that \(\sin \theta \approx \theta\) (in radians) when \(|\theta|\) is small. Physicists often use the approximation \(\sin \theta \approx \theta\) for small values of \(\theta\). For what values of \(\theta\) is the magni

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Proving a Theorem If t is any real number, prove that \(1+(\tan t)^{2}=(\sec t)^{2}\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Taylor Polynomials Radian measure allows the trigonometric functions to be approximated by simple polynomial functions. For example, in Exercises 79 and 80, sine and cosine are approximated by Taylor polynomials, named after the English mathematician Brook Taylor (16851731). Complete each table showi

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Taylor Polynomials Radian measure allows the trigonometric functions to be approximated by simple polynomial functions. For example, in Exercises 79 and 80, sine and cosine are approximated by Taylor polynomials, named after the English mathematician Brook Taylor (16851731). Complete each table showi