 10.2.1E: Plot the points with polar coordinates and . Give two alternative s...
 10.2.2E: Write the equations that are used to express a point with polar coo...
 10.2.3E: Write the equations that are used to express a point with Cartesian...
 10.2.4E: What is the polar equation of a circle of radius ?a? centered at th...
 10.2.5E: What is the polar equation of the vertical line x = 5?
 10.2.6E: What is the polar equation of the horizontal line y = 5?
 10.2.7E: Explain three symmetries in polar graphs and how they are detected ...
 10.2.8E: Explain the Cartesiantopolar method for graphing polar curves.
 10.2.9E: Graph the points with the following polar coordinates. Give two alt...
 10.2.10E: Graph the points with the following polar coordinates. Give two alt...
 10.2.11E: Graph the points with the following polar coordinates. Give two alt...
 10.2.12E: Graph the points with the following polar coordinates. Give two alt...
 10.2.13E: Graph the points with the following polar coordinates. Give two alt...
 10.2.14E: Points in polar coordinates Give two sets of polar coordinates for ...
 10.2.15E: Converting coordinates Express the following polar coordinates in C...
 10.2.16E: Converting coordinates Express the following polar coordinates in C...
 10.2.17E: Converting coordinates Express the following polar coordinates in C...
 10.2.18E: Converting coordinates Express the following polar coordinates in C...
 10.2.19E: Converting coordinates Express the following polar coordinates in C...
 10.2.20E: Converting coordinates Express the following polar coordinates in C...
 10.2.21E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.22E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.23E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.24E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.25E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.26E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.27E: Simple curves Tabulate and plot enough points to sketch a rough gra...
 10.2.28E: Simple curves Tabulate and plot enough points to sketch a rough gra...
 10.2.29E: Simple curves Tabulate and plot enough points to sketch a rough gra...
 10.2.30E: Simple curves Tabulate and plot enough points to sketch a rough gra...
 10.2.31E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.32E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.33E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.34E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.35E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.36E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.37E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.38E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.39E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.40E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.41E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.42E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.43E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.44E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.45E: Matching polar and Cartesian curves A Cartesian and a polar graph o...
 10.2.46E: Matching polar and Cartesian curves A Cartesian and a polar graph o...
 10.2.47E: Matching polar and Cartesian curves A Cartesian and a polar graph o...
 10.2.48E: Matching polar and Cartesian curves A Cartesian and a polar graph o...
 10.2.49E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.50E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.51E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.52E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.53E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.54E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.55E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.56E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.57E: Explain why or why not Determine whether the following statements a...
 10.2.58E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.59E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.60E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.61E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.62E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.63E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.64E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.65E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.66E: Circles in general Show that the polar equation describes a circle ...
 10.2.67E: Circles in general Show that the polar equation describes a circle ...
 10.2.68E: Equations of circles Use the results of Exercises 66–67 to describe...
 10.2.69E: Equations of circles Use the results of Exercise to describe and gr...
 10.2.70E: Equations of circles Use the results of Exercise to describe and gr...
 10.2.71E: Equations of circles Use the results of Exercise to describe and gr...
 10.2.72E: Equations of circles Use the results of Exercise to describe and gr...
 10.2.73E: Equations of circles Use the results of Exercise to describe and gr...
 10.2.74E: Equations of circles Find equations of the circles in the figure. D...
 10.2.75E: Vertical lines Consider the polar curve r = 2 sec ?.a. Graph the cu...
 10.2.76E: Lines in polar coordinatesa. Show that an equation of the line y = ...
 10.2.77E: Equations of lines Use the result of Exercise 76 to describe and gr...
 10.2.78E: Equations of lines Use the result of Exercise 76 to describe and gr...
 10.2.79E: Equations of lines Use the result of Exercise to describe and graph...
 10.2.80E: Equations of lines Use the result of Exercise to describe and graph...
 10.2.81E: The limaçon family The equations r = a + b cos ? and r = a + b sin ...
 10.2.82E: Limiting limaçon Consider the family of limaçons r = 1 + b cos ?. D...
 10.2.83E: The lemniscate family Equations of the form r2 = a sin 2? and r2 = ...
 10.2.84E: The lemniscate family Equations of the form r2 = a sin 2? and r2 = ...
 10.2.85E: The lemniscate family Equations of the form r2 = a sin 2? and r2 = ...
 10.2.86E: The lemniscate family Equations of the form r2 = a sin 2? and r2 = ...
 10.2.87E: The rose family Equations of the form r = a sin m? or r = a cos m?,...
 10.2.88E: The rose family Equations of the form r = a sin m? or r = a cos m?,...
 10.2.89E: The rose family Equations of the form r = a sin m? or r = a cos m?,...
 10.2.90E: The rose family Equations of the form r = a sin m? or r = a cos m?,...
 10.2.91E: Number of rose petals Show that the graph of r = a sin m? or r = a ...
 10.2.92E: Spirals Graph the following spirals. Indicate the direction in whic...
 10.2.93E: Spirals Graph the following spirals. Indicate the direction in whic...
 10.2.94E: Spirals Graph the following spirals. Indicate the direction in whic...
 10.2.95E: Intersection points Points at which the graphs of r = f(?) and r = ...
 10.2.96E: Intersection points Points at which the graphs of r = f(?) and r = ...
 10.2.97E: Intersection points Points at which the graphs of r = f(?) and r = ...
 10.2.98E: Intersection points Points at which the graphs of r = f(?) and r = ...
 10.2.99E: Enhanced butterfly curve The butterfly curve of Example 8 may be en...
 10.2.100E: Finger curves Consider the curve r = f(?) = cos (a?)  1.5, where a...
 10.2.101E: EarthMars system A simplified model assumes that the orbits of Ear...
 10.2.102E: Channel flow Water flows in a shallow semicircular channel with inn...
 10.2.103AE: Special circles Show that the equation r = a cos ? + b sin ?, where...
 10.2.104AE: Cartesian lenmiscate Find the equation in Cartesian coordinates of ...
 10.2.105AE: Subtle symmetry Without using a graphing utility, determine the sym...
 10.2.106AE: Complete curves Consider the polar curve r = cos (n?/m), where n an...
Solutions for Chapter 10.2: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 10.2
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 106 problems in chapter 10.2 have been answered, more than 151780 students have viewed full stepbystep solutions from this chapter. Chapter 10.2 includes 106 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

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

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Common difference
See Arithmetic sequence.

Conversion factor
A ratio equal to 1, used for unit conversion

Cotangent
The function y = cot x

Course
See Bearing.

Deductive reasoning
The process of utilizing general information to prove a specific hypothesis

Direction vector for a line
A vector in the direction of a line in threedimensional space

Identity
An equation that is always true throughout its domain.

Length of a vector
See Magnitude of a vector.

Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + aekx, where a, b, c, and k are positive with b < 1. c is the limit to growth

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Partial fraction decomposition
See Partial fractions.

Placebo
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.

Pole
See Polar coordinate system.

Quantitative variable
A variable (in statistics) that takes on numerical values for a characteristic being measured.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

RRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the righthand end point of each subinterval.

Solve a triangle
To find one or more unknown sides or angles of a triangle

Sum of an infinite series
See Convergence of a series