ssrs barcode font download For curves defined in polar coordinates, PolarPlot is available. in Software

Creation QR Code in Software For curves defined in polar coordinates, PolarPlot is available.

For curves defined in polar coordinates, PolarPlot is available.
Decode QR In None
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
QR Code Generator In None
Using Barcode creation for Software Control to generate, create QR Code image in Software applications.
PolarPlot[f[p], {p, pmin, pmax}] generates a plot of the polar equation r = f ( ) as varies from min to max . PolarPlot[{f1[p], f2[p], ...}, {p, pmin, pmax}] plots several polar graphs on one set of axes.
QR Decoder In None
Using Barcode scanner for Software Control to read, scan read, scan image in Software applications.
Make QR Code ISO/IEC18004 In C#.NET
Using Barcode maker for .NET Control to generate, create QR Code image in .NET applications.
Note: The default aspect ratio for PolarPlot is AspectRatio Automatic.
Generate Quick Response Code In Visual Studio .NET
Using Barcode creator for ASP.NET Control to generate, create QR Code image in ASP.NET applications.
QR-Code Maker In .NET
Using Barcode maker for VS .NET Control to generate, create QR Code 2d barcode image in VS .NET applications.
EXAMPLE 29
Denso QR Bar Code Drawer In VB.NET
Using Barcode printer for .NET Control to generate, create QR Code image in VS .NET applications.
Generate UPC A In None
Using Barcode maker for Software Control to generate, create UPC Code image in Software applications.
PolarPlot[3 (1 Cos[ ]), {p, 0, 2 o}]
Make Bar Code In None
Using Barcode maker for Software Control to generate, create barcode image in Software applications.
Bar Code Generator In None
Using Barcode creator for Software Control to generate, create bar code image in Software applications.
(This curve is called a cardioid.)
Code 128C Creation In None
Using Barcode printer for Software Control to generate, create ANSI/AIM Code 128 image in Software applications.
GS1 - 13 Generator In None
Using Barcode creator for Software Control to generate, create UPC - 13 image in Software applications.
Two-Dimensional Graphics
Print ANSI/AIM ITF 25 In None
Using Barcode drawer for Software Control to generate, create ANSI/AIM ITF 25 image in Software applications.
Paint GTIN - 12 In C#
Using Barcode generator for Visual Studio .NET Control to generate, create UPC A image in Visual Studio .NET applications.
EXAMPLE 30 Plot the three-leaf rose r = sin 3q inside the unit circle r = 1.
Recognizing European Article Number 13 In Visual Basic .NET
Using Barcode scanner for VS .NET Control to read, scan read, scan image in VS .NET applications.
Bar Code Reader In Java
Using Barcode decoder for Java Control to read, scan read, scan image in Java applications.
PolarPlot[{1, Sin[3p]}, {p, 0, 2 o}]
Decode GS1-128 In Visual Basic .NET
Using Barcode scanner for .NET framework Control to read, scan read, scan image in .NET applications.
Encode EAN / UCC - 13 In None
Using Barcode generation for Word Control to generate, create UCC - 12 image in Word applications.
1.0
Print Code 39 Full ASCII In Objective-C
Using Barcode printer for iPad Control to generate, create Code 3/9 image in iPad applications.
Generating Code 3/9 In None
Using Barcode maker for Online Control to generate, create Code 39 Extended image in Online applications.
0.5
0.5
1.0
SOLVED PROBLEMS
4.9 Sketch the parabola y = x2 9 and a circle of radius 3 centered at the origin.
SOLUTION
g1 = Plot[x 2 9,{x, 4,4}]; g2 = Graphics[Circle[{0, 0}, 3]]; g3 = Graphics[Text["CIRCLE IN A PARABOLA", {0, 6},
TextStyle {FontSize 16}]];
Show[g1, g2, g3, AspectRatio Automatic]
CIRCLE IN A PARABOLA 5
Two-Dimensional Graphics
4.10 The curve traced by a point on a circle as the circle rolls along a straight line is called a cycloid and has parametric equations x = r ( sin ), y = r (1 cos ) where r represents the radius of the circle. Plot the cycloid formed as a circle of radius 1 makes four complete revolutions.
SOLUTION
ParametricPlot[{p Sin[p], 1 Cos[p]}, {p, 0, 8 o}, Ticks {Automatic, {0, 1, 2}}]
2 1 0 5 10 15 20 25
4.11 Let P be a point at a distance a from the center of a circle of radius r. (Imagine the point being placed on a spoke of a bicycle wheel.) The curve traced by P as the circle rolls along a straight line is called a trochoid. Its parametric equations are x = r a sin , y = r a cos . Sketch the trochoid with 1 r = 1, a = as the circle makes four revolutions. What would the graph look like if r = 1, a = 2 so 2 that the point is outside the circle
SOLUTION
r = 1; a = 1/2; ParametricPlot[{r p a Sin[p], r a Cos[p]}, {p, 0, 8 o}, PlotRange {Automatic, {0, 2}}, Ticks {Automatic, {0, 1, 2}}]
2 1 0 5 10 15 20 25
r = 1; a = 2; ParametricPlot[{r p a Sin[p], r a Cos[p]}, {p, 0, 8 o}]
3 2 1 5 1 10 15 20 25
4.12 A circle of radius b rolls on the inside of a larger circle of radius a. The curve traced out by a fixed point initially at (a, 0) is called a hypocycloid and has equations
x = (a b)cos + b cos a b b y = (a b)sin b sin a b b
Sketch the hypocycloid for a = 4, b = 1 (0 x 2 ) and then again for a = 8, b = 5 (0 x 10 ).
SOLUTION
x[ _]:= (a b)Cos[ ]+ b Cos a b b y[ _]:= (a b)Sin[ ] b Sin a b b
Two-Dimensional Graphics
a = 4; b = 1; ParametricPlot[{x[ ], y[ ]}, { , 0, 2 o}]
a = 8; b = 5; ParametricPlot[{x[ ], y[ ]}, { , 0, 10 o}]
Two-Dimensional Graphics
4.13 Sketch the graph defined by the equation y 2 = x 3 (2 x ), 0 x 2, 2 y 2.
SOLUTION
ContourPlot[y2 x3(2 x), {x, 0, 2}, {y, 2, 2}, Frame False, Axes True]
4.14 Sketch the graph of the Tschirnhausen cubic: y 2 = x 3 + 3 x 2 , 3 x 3, 8 y 8.
SOLUTION
ContourPlot[y2 x3 + 3x2, {x, 3, 3}, {y, 8, 8}, Axes True, Frame False]
Two-Dimensional Graphics
4.15 The polar graph r = q is called the Spiral of Archimedes. Sketch the graph for 0 10 and then again for 10 10 .
SOLUTION
PolarPlot[p, {p, 0, 10 o}]
PolarPlot[p, {p, 10 o, 10 o}]
10 10
10 10
4.16 The equation r = sin n , where n is a positive integer, represents a family of polar curves called roses. Investigate the behavior of this family and form a conjecture about how the number of loops is related to n.
SOLUTION
g1 = PolarPlot[Sin[2 p], {p, 0, 2 o}, Ticks False, PlotLabel "n = 2"]; g2 = PolarPlot[Sin[3 p], {p, 0, 2 o}, Ticks False, PlotLabel "n = 3"]; g3 = PolarPlot[Sin[4 p], {p, 0, 2 o}, Ticks False, PlotLabel "n = 4"]; g4 = PolarPlot[Sin[5 p], {p, 0, 2 o}, Ticks False, PlotLabel "n = 5"]; GraphicsArray[{{g1, g2}, {g3, g4}}]
n=2 n=3
Conclusion: If n is odd, the rose will have n leaves. If n is even, there will be 2n leaves.
Two-Dimensional Graphics
4.17 Sketch the cardioid r = 1 cos and the circle r = 1 on the same set of axes.
SOLUTION
PolarPlot[{1 Cos[ ], 1}, { , 0, 2 o}]
2.0
1.5
1.0
0.5
0.5
1.0
Copyright © OnBarcode.com . All rights reserved.