 10.3.1: Plot the point whose polar coordinates are given. Then find two oth...
 10.3.2: Plot the point whose polar coordinates are given. Then find two oth...
 10.3.3: Plot the point whose polar coordinates are given. Then find the Car...
 10.3.4: Plot the point whose polar coordinates are given. Then find the Car...
 10.3.5: The Cartesian coordinates of a point are given. (i) Find polar coor...
 10.3.6: The Cartesian coordinates of a point are given. (i) Find polar coor...
 10.3.7: Sketch the region in the plane consisting of points whose polar coo...
 10.3.8: Sketch the region in the plane consisting of points whose polar coo...
 10.3.9: Sketch the region in the plane consisting of points whose polar coo...
 10.3.10: Sketch the region in the plane consisting of points whose polar coo...
 10.3.11: Sketch the region in the plane consisting of points whose polar coo...
 10.3.12: Sketch the region in the plane consisting of points whose polar coo...
 10.3.13: Find the distance between the points with polar coordinates and .
 10.3.14: Find a formula for the distance between the points with polar coord...
 10.3.15: Identify the curve by finding a Cartesian equation for the curve. r...
 10.3.16: Identify the curve by finding a Cartesian equation for the curve. r...
 10.3.17: Identify the curve by finding a Cartesian equation for the curve. r...
 10.3.18: Identify the curve by finding a Cartesian equation for the curve. r...
 10.3.19: Identify the curve by finding a Cartesian equation for the curve. r...
 10.3.20: Identify the curve by finding a Cartesian equation for the curve. r...
 10.3.21: Find a polar equation for the curve represented by the given Cartes...
 10.3.22: Find a polar equation for the curve represented by the given Cartes...
 10.3.23: Find a polar equation for the curve represented by the given Cartes...
 10.3.24: Find a polar equation for the curve represented by the given Cartes...
 10.3.25: Find a polar equation for the curve represented by the given Cartes...
 10.3.26: Find a polar equation for the curve represented by the given Cartes...
 10.3.27: For each of the described curves, decide if the curve would be more...
 10.3.28: For each of the described curves, decide if the curve would be more...
 10.3.29: Sketch the curve with the given polar equation.6 2
 10.3.30: Sketch the curve with the given polar equation. 3r 2 0
 10.3.31: Sketch the curve with the given polar equation.r sin r
 10.3.32: Sketch the curve with the given polar equation.r 3 cos r
 10.3.33: Sketch the curve with the given polar equation.r 21 sin r
 10.3.34: Sketch the curve with the given polar equation.r 1 3 cos r
 10.3.35: Sketch the curve with the given polar equation.r 0 r
 10.3.36: Sketch the curve with the given polar equation.ln 1 r
 10.3.37: Sketch the curve with the given polar equation.r sin 2 r
 10.3.38: Sketch the curve with the given polar equation.r 2 cos 3 3
 10.3.39: Sketch the curve with the given polar equation.r 2 cos 4 r
 10.3.40: Sketch the curve with the given polar equation.sin 5 r
 10.3.41: Sketch the curve with the given polar equation.r 2 sin 2 2 4 cos 2
 10.3.42: Sketch the curve with the given polar equation.2 sin 2 2
 10.3.43: Sketch the curve with the given polar equation.r 2 cos 32 1
 10.3.44: Sketch the curve with the given polar equation.r 1r
 10.3.45: Sketch the curve with the given polar equation.r 1 2 cos 2 r
 10.3.46: Sketch the curve with the given polar equation.r 1 2 cos2 r 2
 10.3.47: The figure shows the graph of as a function of in Cartesian coordin...
 10.3.48: The figure shows the graph of as a function of in Cartesian coordin...
 10.3.49: Show that the polar curve (called a conchoid) has the line as a ver...
 10.3.50: Show that the curve (also a conchoid) has the line as a horizontal ...
 10.3.51: Show that the curve (called a cissoid of Diocles) has the line as a...
 10.3.52: Sketch the curve .
 10.3.53: (a) In Example 11 the graphs suggest that the limaon has an inner l...
 10.3.54: Match the polar equations with the graphs labeled IVI. Give reasons...
 10.3.55: Find the slope of the tangent line to the given polar curve at the ...
 10.3.56: Find the slope of the tangent line to the given polar curve at the ...
 10.3.57: Find the slope of the tangent line to the given polar curve at the ...
 10.3.58: Find the slope of the tangent line to the given polar curve at the ...
 10.3.59: Find the slope of the tangent line to the given polar curve at the ...
 10.3.60: Find the slope of the tangent line to the given polar curve at the ...
 10.3.61: Find the points on the given curve where the tangent line is horizo...
 10.3.62: Find the points on the given curve where the tangent line is horizo...
 10.3.63: Find the points on the given curve where the tangent line is horizo...
 10.3.64: Find the points on the given curve where the tangent line is horizo...
 10.3.65: Find the points on the given curve where the tangent line is horizo...
 10.3.66: Find the points on the given curve where the tangent line is horizo...
 10.3.67: Show that the polar equation , where , represents a circle, and fin...
 10.3.68: Show that the curves and intersect at right angles.
 10.3.69: Use a graphing device to graph the polar curve. Choose the paramete...
 10.3.70: Use a graphing device to graph the polar curve. Choose the paramete...
 10.3.71: Use a graphing device to graph the polar curve. Choose the paramete...
 10.3.72: Use a graphing device to graph the polar curve. Choose the paramete...
 10.3.73: Use a graphing device to graph the polar curve. Choose the paramete...
 10.3.74: Use a graphing device to graph the polar curve. Choose the paramete...
 10.3.75: How are the graphs of and related to the graph of ? In general, how...
 10.3.76: Use a graph to estimate the coordinate of the highest points on th...
 10.3.77: (a) Investigate the family of curves defined by the polar equations...
 10.3.78: A family of curves is given by the equations , where is a real numb...
 10.3.79: A family of curves has polar equations r 1 a cos 1 a cos Investigat...
 10.3.80: The astronomer Giovanni Cassini (16251712) studied the family of cu...
 10.3.81: Let be any point (except the origin) on the curve . If is the angle...
 10.3.82: (a) Use Exercise 81 to show that the angle between the tangent line...
Solutions for Chapter 10.3: Polar Coordinates
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 10.3: Polar Coordinates
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 10.3: Polar Coordinates includes 82 full stepbystep solutions. Since 82 problems in chapter 10.3: Polar Coordinates have been answered, more than 43757 students have viewed full stepbystep solutions from this chapter. Calculus, was written by and is associated to the ISBN: 9780534393397. This textbook survival guide was created for the textbook: Calculus,, edition: 5.

Absolute maximum
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

Acceleration due to gravity
g ? 32 ft/sec2 ? 9.8 m/sec

Addition property of inequality
If u < v , then u + w < v + w

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Arithmetic sequence
A sequence {an} in which an = an1 + d for every integer n ? 2 . The number d is the common difference.

Bias
A flaw in the design of a sampling process that systematically causes the sample to differ from the population with respect to the statistic being measured. Undercoverage bias results when the sample systematically excludes one or more segments of the population. Voluntary response bias results when a sample consists only of those who volunteer their responses. Response bias results when the sampling design intentionally or unintentionally influences the responses

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Degree
Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

Descriptive statistics
The gathering and processing of numerical information

Difference of complex numbers
(a + bi)  (c + di) = (a  c) + (b  d)i

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Inequality symbol or
<,>,<,>.

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

Negative numbers
Real numbers shown to the left of the origin on a number line.

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

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Stemplot (or stemandleaf plot)
An arrangement of a numerical data set into a specific tabular format.

Unbounded interval
An interval that extends to ? or ? (or both).