 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 84648 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.

Augmented matrix
A matrix that represents a system of equations.

Central angle
An angle whose vertex is the center of a circle

Conditional probability
The probability of an event A given that an event B has already occurred

Constant term
See Polynomial function

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Extracting square roots
A method for solving equations in the form x 2 = k.

Feasible points
Points that satisfy the constraints in a linear programming problem.

Geometric series
A series whose terms form a geometric sequence.

Graphical model
A visible representation of a numerical or algebraic model.

Halfangle identity
Identity involving a trigonometric function of u/2.

Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Mode of a data set
The category or number that occurs most frequently in the set.

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Pointslope form (of a line)
y  y1 = m1x  x 12.

Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.

Real number
Any number that can be written as a decimal.

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

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