Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find the absolute maximum value and absolute minimum value in [0, 2\(\pi\)] and where they occur. \(y=3 \cos 2 x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find the absolute maximum value and absolute minimum value in [0, 2\(\pi\)] and where they occur. \(y=2+3 \cos x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find the absolute maximum value and absolute minimum value in [0, 2\(\pi\)] and where they occur. \(y=2 \sqrt{\cos 2 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find the absolute maximum value and absolute minimum value in [0, 2\(\pi\)] and where they occur. \(y=3-3 \sin x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 and 6, determine if the graph of the function is symmetric about the (a) x-axis, (b) y-axis, and (c) origin. \(y=\sin 2 x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 and 6, determine if the graph of the function is symmetric about the (a) x-axis, (b) y-axis, and (c) origin. \(y=\cos 4 x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7-10, use trig identities to simplify the expression. \(\sin (\pi-\theta)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7-10, use trig identities to simplify the expression. \(\cos (\pi-\theta) \)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7-10, use trig identities to simplify the expression. \(\cos 2(\pi+\theta)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7-10, use trig identities to simplify the expression. \(\sin 2(\pi+\theta)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, (a) complete the table for the polar equation, and (b) plot the corresponding points. \(r=3 \cos 2 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, (a) complete the table for the polar equation, and (b) plot the corresponding points. \(r=2 \sin 3 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 36, draw a graph of the rose curve. State the smallest \(\theta \text {-interval }(0 \leq \theta \leq k)\) that will produce a complete graph. \(r=3 \sin 3 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 36, draw a graph of the rose curve. State the smallest \(\theta \text {-interval }(0 \leq \theta \leq k)\) that will produce a complete graph. \(r=-3 \cos 2 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3-6, draw a graph of the rose curve. State the smallest \(\theta \text {-interval }(0 \leq \theta \leq k)\) that will produce a complete graph. \(r=3 \cos 2 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3-6, draw a graph of the rose curve. State the smallest \(\theta \text {-interval }(0 \leq \theta \leq k)\) that will produce a complete graph. \(r=3 \sin 5 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 7 and 8 refer to the curves in the given figure. The graphs of which equations are shown? \(r_{1}=3 \cos 6 \theta \quad r_{2}=3 \sin 8 \theta \quad r_{3}=3|\cos 3 \theta|\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 7 and 8 refer to the curves in the given figure. Use trigonometric identities to explain which of these curves is the graph of \(r=6 \cos 2 \theta \sin 2 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, match the equation with its graph without using your graphing calculator. Does the graph of \(r=2+2 \sin \theta \text { or } r=2-2 \cos \theta\) appear in the figure? Explain.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, match the equation with its graph without using your graphing calculator. Does the graph of \(r=2+3 \cos \theta \text { or } r=2-3 \cos \theta\) appear in the figure? Explain.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, match the equation with its graph without using your graphing calculator. Is the graph in (a) the graph of \(r=2-2 \sin \theta\) or \(r=2+2 \cos \theta\)? Explain.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, match the equation with its graph without using your graphing calculator. Is the graph in (a) the graph of \(r=2+1.5 \cos \theta\) or \(r=2-1.5 \sin \theta\)? Explain.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1320, use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin. Support your algebraic solution with a grapher. \(r=3+3 \sin \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1320, use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin. Support your algebraic solution with a grapher. \(r=1+2 \cos \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1320, use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin. Support your algebraic solution with a grapher. \(r=4-3 \cos \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1320, use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin. Support your algebraic solution with a grapher. \(r=1-3 \sin \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1320, use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin. Support your algebraic solution with a grapher. \(r=5 \cos 2 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1320, use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin. Support your algebraic solution with a grapher. \(r=7 \sin 3 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1320, use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin. Support your algebraic solution with a grapher. \(r=\frac{3}{1+\sin \theta}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1320, use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin. Support your algebraic solution with a grapher. \(r=\frac{2}{1-\cos \theta}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, identify the points for \(0 \leq \theta \leq 2 \pi\) where maximum r-values occur on the graph of the polar equation. \(r=2+3 \cos \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, identify the points for \(0 \leq \theta \leq 2 \pi\) where maximum r-values occur on the graph of the polar equation. \(r=-3+2 \sin \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, identify the points for \(0 \leq \theta \leq 2 \pi\) where maximum r-values occur on the graph of the polar equation. \(r=3 \cos 3 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, identify the points for \(0 \leq \theta \leq 2 \pi\) where maximum r-values occur on the graph of the polar equation. \(r=4 \sin 2 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. r=3

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. r= -2

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(\theta=\pi / 3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(\theta=-\pi / 4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=2 \sin 3 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=-3 \cos 4 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=5+4 \sin \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=6-5 \cos \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=4+4 \cos \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=5-5 \sin \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=5+2 \cos \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=3-\sin \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=2+5 \cos \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=3-4 \sin \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=1-\cos \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=2+\sin \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=2 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r=\theta / 4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r^{2}=\sin 2 \theta, 0 \leq \theta \leq 2 \pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2544, analyze the graph of the polar curve. \(r^{2}=9 \cos 2 \theta, 0 \leq \theta \leq 2 \pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, find the length of each petal of the polar curve. \(r=2+4 \sin 2 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, find the length of each petal of the polar curve. \(r=3-5 \cos 2 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, find the length of each petal of the polar curve. \(r=1-4 \cos 5 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, find the length of each petal of the polar curve. \(r=3+4 \sin 5 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, select the two equations whose graphs are the same curve. Then, even though the graphs of the equations are identical, describe how the two paths are different as \(\theta\) increases from 0 to 2\(\pi\). \(r_{1}=1+3 \sin \theta, \quad r_{2}=-1+3 \sin \theta, \quad r_{3}=1-3 \si

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, select the two equations whose graphs are the same curve. Then, even though the graphs of the equations are identical, describe how the two paths are different as \(\theta\) increases from 0 to 2\(\pi\). \(r_{1}=1+2 \cos \theta, \quad r_{2}=-1-2 \cos \theta, \quad r_{3}=-1+2 \c

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, select the two equations whose graphs are the same curve. Then, even though the graphs of the equations are identical, describe how the two paths are different as \(\theta\) increases from 0 to 2\(\pi\). \(r_{1}=1+2 \cos \theta, \quad r_{2}=1-2 \cos \theta, \quad r_{3}=-1 - 2 \

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, select the two equations whose graphs are the same curve. Then, even though the graphs of the equations are identical, describe how the two paths are different as \(\theta\) increases from 0 to 2\(\pi\). \(r_{1}=2+2 \sin \theta, \quad r_{2}=-2+2 \sin \theta, \quad r_{3}=2-2 \si

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, (a) describe the graph of the polar equation, (b) state any symmetry that the graph possesses, and (c) state its maximum r-value if it exists. \(r=2 \sin ^{2} 2 \theta+\sin 2 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, (a) describe the graph of the polar equation, (b) state any symmetry that the graph possesses, and (c) state its maximum r-value if it exists. \(r=3 \cos 2 \theta-\sin 3 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, (a) describe the graph of the polar equation, (b) state any symmetry that the graph possesses, and (c) state its maximum r-value if it exists. \(r=1-3 \cos 3 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, (a) describe the graph of the polar equation, (b) state any symmetry that the graph possesses, and (c) state its maximum r-value if it exists. \(r=1+3 \sin 3 \theta\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Analyze the graphs of the polar equations \(r=a \cos n \theta \text { and } r=a \sin n \theta\) when n is an even integer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Revisiting Example 4 Use the polar symmetry tests to prove that the graph of the curve \(r=3 \sin 4 \theta\) is symmetric about the y-axis and the origin.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Revisiting Example 5 Confirm the range stated for the polar function \(r=3-3 \sin \theta\) of Example 5 by graphing for \(y=3-3 \sin x \text { for } 0 \leq x \leq 2 \pi\). Explain why this works.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Revisiting Example 6 Confirm the range stated for the polar function \(r=2+3 \cos \theta\) of Example 6 by graphing for \(y=2+3 \cos x \text { for } 0 \leq x \leq 2 \pi \text {. }\) Explain why this works.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False A polar curve is always bounded. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The graph of \(r=2+\cos \theta\) is symmetric about the x-axis. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following gives the number of petals of the rose curve \(r=3 \cos 2 \theta\)? (A) 1 (B) 2 (C) 3 (D) 4 (E) 6

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following describes the symmetry of the rose graph of \(r=3 \cos 2 \theta\) (A) Only the x-axis (B) Only the y-axis (C) Only the origin (D) The x-axis, the y-axis, the origin (E) Not symmetric about the x-axis, the y-axis, or the origin

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following is a maximum r-value for \(r=2-3 \cos \theta\)? (A) 6 (B) 5 (C) 3 (D) 2 (E) 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following is the number of petals of the rose curve \(r=5 \sin 3 \theta^{\circ}\)? (A) 1 (B) 3 (C) 6 (D) 10 (E) 15

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Analyzing Rose Curves Consider the polar equation \(r=a \cos n \theta\) for n, an odd integer. (a) Prove that the graph is symmetric about the x-axis. (b) Prove that the graph is not symmetric about the y-axis. (c) Prove that the graph is not symmetric about the origin. (d) Prove

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Analyzing Rose Curves Consider the polar equation \(r=a \sin n \theta\) for n, an odd integer. (a) Prove that the graph is symmetric about the x-axis. (b) Prove that the graph is not symmetric about the y-axis. (c) Prove that the graph is not symmetric about the origin. (d) Prove

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Extended Rose Curves The graphs of \(r_{1}=3 \sin ((7 / 2) \theta) \text { and } r_{2}=3 \sin ((7 / 2) \theta)\) may be called rose curves. (a) Determine the smallest \(\theta\)-interval that will produce a complete graph of r1; of r2. (b) How many petals does each graph have?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 70-72, graph each polar equation. Describe how they are related to each other. (a) \(r_{1}=3 \sin 3 \theta\) (b) \(r_{2}=3 \sin 3\left(\theta+\frac{\pi}{12}\right)\) (c) \( r_{3}=3 \sin 3\left(\theta+\frac{\pi}{4}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 70-72, graph each polar equation. Describe how they are related to each other. (a) \(r_{1}=2 \sec \theta\) (b) (c)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 70-72, graph each polar equation. Describe how they are related to each other. (a) \(r_{1}=2-2 \cos \theta\) (b) \( r_{2}=r_{1}\left(\theta+\frac{\pi}{4}\right)\) (c) \(r_{3}=r_{1}\left(\theta+\frac{\pi}{3}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Describe how the graphs of \(r=f(\theta)\), \(r=f(\theta+\alpha), \text { and } r=f(\theta-\alpha)\) are related. Explain why you think this generalization is true.