 10.4.1: In Exercises 16, plot the point in polar coordinates and find the c...
 10.4.2: In Exercises 16, plot the point in polar coordinates and find the c...
 10.4.3: In Exercises 16, plot the point in polar coordinates and find the c...
 10.4.4: In Exercises 16, plot the point in polar coordinates and find the c...
 10.4.5: In Exercises 16, plot the point in polar coordinates and find the c...
 10.4.6: In Exercises 16, plot the point in polar coordinates and find the c...
 10.4.7: In Exercises 710, use the feature of a graphing utility to find the...
 10.4.8: In Exercises 710, use the feature of a graphing utility to find the...
 10.4.9: In Exercises 710, use the feature of a graphing utility to find the...
 10.4.10: In Exercises 710, use the feature of a graphing utility to find the...
 10.4.11: In Exercises 1116, the rectangular coordinates of a point are given...
 10.4.12: In Exercises 1116, the rectangular coordinates of a point are given...
 10.4.13: In Exercises 1116, the rectangular coordinates of a point are given...
 10.4.14: In Exercises 1116, the rectangular coordinates of a point are given...
 10.4.15: In Exercises 1116, the rectangular coordinates of a point are given...
 10.4.16: In Exercises 1116, the rectangular coordinates of a point are given...
 10.4.17: In Exercises 1720, use the feature of a graphing utility to find on...
 10.4.18: In Exercises 1720, use the feature of a graphing utility to find on...
 10.4.19: In Exercises 1720, use the feature of a graphing utility to find on...
 10.4.20: In Exercises 1720, use the feature of a graphing utility to find on...
 10.4.21: Plot the point if the point is given in (a) rectangular coordinates...
 10.4.22: Graphical Reasoning (a) Set the window format of a graphing utility...
 10.4.23: In Exercises 2326, match the graph with its polar equation. [The gr...
 10.4.24: In Exercises 2326, match the graph with its polar equation. [The gr...
 10.4.25: In Exercises 2326, match the graph with its polar equation. [The gr...
 10.4.26: In Exercises 2326, match the graph with its polar equation. [The gr...
 10.4.27: In Exercises 2734, convert the rectangular equation to polar form a...
 10.4.28: In Exercises 2734, convert the rectangular equation to polar form a...
 10.4.29: In Exercises 2734, convert the rectangular equation to polar form a...
 10.4.30: In Exercises 2734, convert the rectangular equation to polar form a...
 10.4.31: In Exercises 2734, convert the rectangular equation to polar form a...
 10.4.32: In Exercises 2734, convert the rectangular equation to polar form a...
 10.4.33: In Exercises 2734, convert the rectangular equation to polar form a...
 10.4.34: In Exercises 2734, convert the rectangular equation to polar form a...
 10.4.35: In Exercises 35 42, convert the polar equation to rectangular form ...
 10.4.36: In Exercises 35 42, convert the polar equation to rectangular form ...
 10.4.37: In Exercises 35 42, convert the polar equation to rectangular form ...
 10.4.38: In Exercises 35 42, convert the polar equation to rectangular form ...
 10.4.39: In Exercises 35 42, convert the polar equation to rectangular form ...
 10.4.40: In Exercises 35 42, convert the polar equation to rectangular form ...
 10.4.41: In Exercises 35 42, convert the polar equation to rectangular form ...
 10.4.42: In Exercises 35 42, convert the polar equation to rectangular form ...
 10.4.43: In Exercises 4352, use a graphing utility to graph the polar equati...
 10.4.44: In Exercises 4352, use a graphing utility to graph the polar equati...
 10.4.45: In Exercises 4352, use a graphing utility to graph the polar equati...
 10.4.46: In Exercises 4352, use a graphing utility to graph the polar equati...
 10.4.47: In Exercises 4352, use a graphing utility to graph the polar equati...
 10.4.48: In Exercises 4352, use a graphing utility to graph the polar equati...
 10.4.49: In Exercises 4352, use a graphing utility to graph the polar equati...
 10.4.50: In Exercises 4352, use a graphing utility to graph the polar equati...
 10.4.51: In Exercises 4352, use a graphing utility to graph the polar equati...
 10.4.52: In Exercises 4352, use a graphing utility to graph the polar equati...
 10.4.53: Convert the equation to rectangular form and verify that it is the ...
 10.4.54: Distance Formula (a) Verify that the Distance Formula for the dista...
 10.4.55: In Exercises 5558, use the result of Exercise 54 to approximate the...
 10.4.56: In Exercises 5558, use the result of Exercise 54 to approximate the...
 10.4.57: In Exercises 5558, use the result of Exercise 54 to approximate the...
 10.4.58: In Exercises 5558, use the result of Exercise 54 to approximate the...
 10.4.59: In Exercises 59 and 60, find and the slopes of the tangent lines sh...
 10.4.60: In Exercises 59 and 60, find and the slopes of the tangent lines sh...
 10.4.61: In Exercises 6164, use a graphing utility to (a) graph the polar eq...
 10.4.62: In Exercises 6164, use a graphing utility to (a) graph the polar eq...
 10.4.63: In Exercises 6164, use a graphing utility to (a) graph the polar eq...
 10.4.64: In Exercises 6164, use a graphing utility to (a) graph the polar eq...
 10.4.65: In Exercises 65 and 66, find the points of horizontal and vertical ...
 10.4.66: In Exercises 65 and 66, find the points of horizontal and vertical ...
 10.4.67: In Exercises 67 and 68, find the points of horizontal tangency (if ...
 10.4.68: In Exercises 67 and 68, find the points of horizontal tangency (if ...
 10.4.69: In Exercises 6972, use a graphing utility to graph the polar equati...
 10.4.70: In Exercises 6972, use a graphing utility to graph the polar equati...
 10.4.71: In Exercises 6972, use a graphing utility to graph the polar equati...
 10.4.72: In Exercises 6972, use a graphing utility to graph the polar equati...
 10.4.73: In Exercises 7380, sketch a graph of the polar equation and find th...
 10.4.74: In Exercises 7380, sketch a graph of the polar equation and find th...
 10.4.75: In Exercises 7380, sketch a graph of the polar equation and find th...
 10.4.76: In Exercises 7380, sketch a graph of the polar equation and find th...
 10.4.77: In Exercises 7380, sketch a graph of the polar equation and find th...
 10.4.78: In Exercises 7380, sketch a graph of the polar equation and find th...
 10.4.79: In Exercises 7380, sketch a graph of the polar equation and find th...
 10.4.80: In Exercises 7380, sketch a graph of the polar equation and find th...
 10.4.81: In Exercises 8192, sketch a graph of the polar equation.r 5
 10.4.82: In Exercises 8192, sketch a graph of the polar equation.
 10.4.83: In Exercises 8192, sketch a graph of the polar equation.
 10.4.84: In Exercises 8192, sketch a graph of the polar equation.r 1 sin
 10.4.85: In Exercises 8192, sketch a graph of the polar equation.
 10.4.86: In Exercises 8192, sketch a graph of the polar equation.
 10.4.87: In Exercises 8192, sketch a graph of the polar equation.r 3 csc
 10.4.88: In Exercises 8192, sketch a graph of the polar equation. 62 sin 3 c...
 10.4.89: In Exercises 8192, sketch a graph of the polar equation.r 2
 10.4.90: In Exercises 8192, sketch a graph of the polar equation.r 1
 10.4.91: In Exercises 8192, sketch a graph of the polar equation.
 10.4.92: In Exercises 8192, sketch a graph of the polar equation.r r 2 4 sin
 10.4.93: In Exercises 93 96, use a graphing utility to graph the equation an...
 10.4.94: In Exercises 93 96, use a graphing utility to graph the equation an...
 10.4.95: In Exercises 93 96, use a graphing utility to graph the equation an...
 10.4.96: In Exercises 93 96, use a graphing utility to graph the equation an...
 10.4.97: Describe the differences between the rectangular coordinate system ...
 10.4.98: Give the equations for the coordinate conversion from rectangular t...
 10.4.99: For constants and describe the graphs of the equations and in polar...
 10.4.100: How are the slopes of tangent lines determined in polar coordinates...
 10.4.101: Sketch the graph of over each interval.
 10.4.102: Think About It Use a graphing utility to graph the polar equation f...
 10.4.103: Verify that if the curve whose polar equation is is rotated about t...
 10.4.104: The polar form of an equation for a curve is Show that the form bec...
 10.4.105: In Exercises 105108, use the results of Exercises 103 and 104.Write...
 10.4.106: In Exercises 105108, use the results of Exercises 103 and 104.Write...
 10.4.107: In Exercises 105108, use the results of Exercises 103 and 104.Sketc...
 10.4.108: In Exercises 105108, use the results of Exercises 103 and 104.ove t...
 10.4.109: In Exercises 109114, use the result of Exercise 108 to find the ang...
 10.4.110: In Exercises 109114, use the result of Exercise 108 to find the ang...
 10.4.111: In Exercises 109114, use the result of Exercise 108 to find the ang...
 10.4.112: In Exercises 109114, use the result of Exercise 108 to find the ang...
 10.4.113: In Exercises 109114, use the result of Exercise 108 to find the ang...
 10.4.114: In Exercises 109114, use the result of Exercise 108 to find the ang...
 10.4.115: True or False? In Exercises 115118, determine whether the statement...
 10.4.116: True or False? In Exercises 115118, determine whether the statement...
 10.4.117: True or False? In Exercises 115118, determine whether the statement...
 10.4.118: True or False? In Exercises 115118, determine whether the statement...
Solutions for Chapter 10.4: Polar Coordinates and Polar Graphs
Full solutions for Calculus: Early Transcendental Functions  4th Edition
ISBN: 9780618606245
Solutions for Chapter 10.4: Polar Coordinates and Polar Graphs
Get Full SolutionsChapter 10.4: Polar Coordinates and Polar Graphs includes 118 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245. Since 118 problems in chapter 10.4: Polar Coordinates and Polar Graphs have been answered, more than 39027 students have viewed full stepbystep solutions from this chapter.

Aphelion
The farthest point from the Sun in a planet’s orbit

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Double inequality
A statement that describes a bounded interval, such as 3 ? x < 5

Independent variable
Variable representing the domain value of a function (usually x).

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

Midpoint (on a number line)
For the line segment with endpoints a and b, a + b2

Multiplication property of equality
If u = v and w = z, then uw = vz

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

Polynomial interpolation
The process of fitting a polynomial of degree n to (n + 1) points.

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Range of a function
The set of all output values corresponding to elements in the domain.

Real part of a complex number
See Complex number.

Reference triangle
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the xaxis, and a perpendicular dropped from a point on the terminal side to the xaxis. The angle in a reference triangle at the origin is the reference angle

Resistant measure
A statistical measure that does not change much in response to outliers.

Response variable
A variable that is affected by an explanatory variable.

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Transformation
A function that maps real numbers to real numbers.

Zero factorial
See n factorial.