 10.3.1: 12 Plot the point whose polar coordinates are given. Then find two ...
 10.3.2: 12 Plot the point whose polar coordinates are given. Then find two ...
 10.3.3: 34 Plot the point whose polar coordinates are given. Then find the ...
 10.3.4: 34 Plot the point whose polar coordinates are given. Then find the ...
 10.3.5: 56 The Cartesian coordinates of a point are given. (i) Find polar c...
 10.3.6: 56 The Cartesian coordinates of a point are given. (i) Find polar c...
 10.3.7: 712 Sketch the region in the plane consisting of points whose polar...
 10.3.8: 712 Sketch the region in the plane consisting of points whose polar...
 10.3.9: 712 Sketch the region in the plane consisting of points whose polar...
 10.3.10: 712 Sketch the region in the plane consisting of points whose polar...
 10.3.11: 712 Sketch the region in the plane consisting of points whose polar...
 10.3.12: 712 Sketch the region in the plane consisting of points whose polar...
 10.3.13: Find the distance between the points with polar coordinates s4, 4y3...
 10.3.14: Find a formula for the distance between the points with polar coord...
 10.3.15: 1520 Identify the curve by finding a Cartesian equation for the curve.
 10.3.16: 1520 Identify the curve by finding a Cartesian equation for the curve.
 10.3.17: 1520 Identify the curve by finding a Cartesian equation for the curve.
 10.3.18: 1520 Identify the curve by finding a Cartesian equation for the curve.
 10.3.19: 1520 Identify the curve by finding a Cartesian equation for the curve.
 10.3.20: 1520 Identify the curve by finding a Cartesian equation for the curve.
 10.3.21: 2126 Find a polar equation for the curve represented by the given C...
 10.3.22: 2126 Find a polar equation for the curve represented by the given C...
 10.3.23: 2126 Find a polar equation for the curve represented by the given C...
 10.3.24: 2126 Find a polar equation for the curve represented by the given C...
 10.3.25: 2126 Find a polar equation for the curve represented by the given C...
 10.3.26: 2126 Find a polar equation for the curve represented by the given C...
 10.3.27: 2728 For each of the described curves, decide if the curve would be...
 10.3.28: 2728 For each of the described curves, decide if the curve would be...
 10.3.29: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.30: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.31: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.32: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.33: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.34: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.35: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.36: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.37: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.38: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.39: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.40: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.41: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.42: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.43: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.44: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.45: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.46: 2946 Sketch the curve with the given polar equation by first sketch...
 10.3.47: 4748 The figure shows a graph of r as a function of in Cartesian co...
 10.3.48: 4748 The figure shows a graph of r as a function of in Cartesian co...
 10.3.49: 4748 The figure shows a graph of r as a function of in Cartesian co...
 10.3.50: 4748 The figure shows a graph of r as a function of in Cartesian co...
 10.3.51: Show that the curve r sin tan (called a cissoid of Diocles) has the...
 10.3.52: Sketch the curve sx 2 1 y 2 d 3 4x 2 y 2
 10.3.53: (a) In Example 11 the graphs suggest that the limaon r 1 1 c sin ha...
 10.3.54: (a) In Example 11 the graphs suggest that the limaon r 1 1 c sin ha...
 10.3.55: 5560 Find the slope of the tangent line to the given polar curve at...
 10.3.56: 5560 Find the slope of the tangent line to the given polar curve at...
 10.3.57: 5560 Find the slope of the tangent line to the given polar curve at...
 10.3.58: 5560 Find the slope of the tangent line to the given polar curve at...
 10.3.59: 5560 Find the slope of the tangent line to the given polar curve at...
 10.3.60: 5560 Find the slope of the tangent line to the given polar curve at...
 10.3.61: 6164 Find the points on the given curve where the tangent line is h...
 10.3.62: 6164 Find the points on the given curve where the tangent line is h...
 10.3.63: 6164 Find the points on the given curve where the tangent line is h...
 10.3.64: 6164 Find the points on the given curve where the tangent line is h...
 10.3.65: Show that the polar equation r a sin 1 b cos , where ab 0, represen...
 10.3.66: Show that the curves r a sin and r a cos intersect at right angles.
 10.3.67: Show that the curves r a sin and r a cos intersect at right angles.
 10.3.68: Show that the curves r a sin and r a cos intersect at right angles.
 10.3.69: Show that the curves r a sin and r a cos intersect at right angles.
 10.3.70: Show that the curves r a sin and r a cos intersect at right angles.
 10.3.71: Show that the curves r a sin and r a cos intersect at right angles.
 10.3.72: Show that the curves r a sin and r a cos intersect at right angles.
 10.3.73: How are the graphs of r 1 1 sins 2 y6d and r 1 1 sins 2 y3d related...
 10.3.74: Use a graph to estimate the ycoordinate of the highest points on t...
 10.3.75: Use a graph to estimate the ycoordinate of the highest points on t...
 10.3.76: Investigate the family of polar curves r 1 1 cosn
 10.3.77: Let P be any point (except the origin) on the curve r fsd. If is th...
 10.3.78: a) Use Exercise 77 to show that the angle between the tangent line ...
Solutions for Chapter 10.3: Polar Coordinates
Full solutions for Single Variable Calculus: Early Transcendentals  8th Edition
ISBN: 9781305270336
Solutions for Chapter 10.3: Polar Coordinates
Get Full SolutionsSingle Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. Since 78 problems in chapter 10.3: Polar Coordinates have been answered, more than 39806 students have viewed full stepbystep solutions from this chapter. Chapter 10.3: Polar Coordinates includes 78 full stepbystep solutions.

Acute angle
An angle whose measure is between 0° and 90°

Axis of symmetry
See Line of symmetry.

Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

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

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Eccentricity
A nonnegative number that specifies how offcenter the focus of a conic is

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.

Limit to growth
See Logistic growth function.

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

Octants
The eight regions of space determined by the coordinate planes.

Present value of an annuity T
he net amount of your money put into an annuity.

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

Quadratic regression
A procedure for fitting a quadratic function to a set of data.

Real number line
A horizontal line that represents the set of real numbers.

Unit circle
A circle with radius 1 centered at the origin.

Weights
See Weighted mean.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.