# vb.net generate qr code cos (p /3) = 1/2 and cos p = 1 in Visual Studio .NET Encode USS Code 39 in Visual Studio .NET cos (p /3) = 1/2 and cos p = 1

cos (p /3) = 1/2 and cos p = 1
Recognizing Code 39 Full ASCII In .NET Framework
Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in Visual Studio .NET applications.
ANSI/AIM Code 39 Creation In Visual Studio .NET
Using Barcode creator for VS .NET Control to generate, create Code 39 Full ASCII image in .NET applications.
Spherical Conversions
USS Code 39 Reader In .NET
Using Barcode recognizer for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications.
Drawing Bar Code In VS .NET
Using Barcode generation for Visual Studio .NET Control to generate, create bar code image in Visual Studio .NET applications.
For things to work without ambiguity when we go the other way, we want the arccosine to be a true function To do that, we must restrict its range (output) to an interval where we don t get into trouble with ambiguity By convention, mathematicians specify the closed interval [0,p] for this purpose That happens to be the ideal range of values for our vertical angle f in spherical coordinates When we make this restriction, we capitalize the A and write Arccosine or Arccos to indicate that we re working with a true function Then we can state the above facts in reverse using the Arccosine function, getting Arccos 1/2 = p /3 and Arccos ( 1) = p For any real number u, we can be sure that Arccos (cos u) = u Going the other way, for any real number v such that 1 v 1, we know that cos (Arccos v) = v We restrict v because the Arccosine function is not defined for input values less than 1 or larger than 1
Recognize Bar Code In .NET
Using Barcode decoder for .NET framework Control to read, scan read, scan image in VS .NET applications.
Painting Code 3/9 In C#.NET
Using Barcode creation for .NET framework Control to generate, create Code-39 image in .NET applications.
Cartesian to spherical: finding e We ve learned how to find the vertical angle on the basis of the Cartesian coordinate z That formula is
Paint Code39 In VS .NET
Using Barcode drawer for ASP.NET Control to generate, create Code 39 Extended image in ASP.NET applications.
Drawing Code 39 In VB.NET
Using Barcode encoder for .NET Control to generate, create Code 39 Full ASCII image in Visual Studio .NET applications.
z = r cos f We can use algebra to rearrange this, getting cos f = z /r provided r 0 When we examine Fig 9-9, we can see that for any given point P, the absolute value of z can never exceed r, so we can be sure that 1 z /r 1 Therefore, we can take the Arccosine of both sides of the preceding equation, getting Arccos (cos f) = Arccos (z /r) Simplifying, we obtain f = Arccos (z /r)
Data Matrix Maker In .NET Framework
Using Barcode generation for .NET framework Control to generate, create Data Matrix ECC200 image in VS .NET applications.
UPC-A Supplement 2 Generator In .NET Framework
Using Barcode maker for .NET framework Control to generate, create UPCA image in VS .NET applications.
Alternative Three-Space
Generate Bar Code In .NET Framework
Using Barcode printer for .NET Control to generate, create bar code image in Visual Studio .NET applications.
Draw EAN 8 In Visual Studio .NET
Using Barcode creation for .NET Control to generate, create EAN8 image in .NET framework applications.
This formula works nicely if we know the value of r But we sometimes want to find the vertical angle in terms of x, y, and z exclusively We ve found that r = (x2 + y2 + z2)1/2 so we can substitute to obtain f = Arccos [z / (x2 + y2 + z2)1/2]
Data Matrix Encoder In None
Using Barcode encoder for Online Control to generate, create Data Matrix 2d barcode image in Online applications.
ECC200 Drawer In None
Using Barcode drawer for Microsoft Word Control to generate, create DataMatrix image in Word applications.
An example Consider a point P in spherical three-space whose coordinates are given by
GS1 - 13 Maker In Java
Using Barcode creator for Java Control to generate, create EAN 13 image in Java applications.
ECC200 Printer In Java
Using Barcode printer for Java Control to generate, create DataMatrix image in Java applications.
P = (q,f,r) = (3p /2,p /2,5) Let s find the equivalent coordinates in Cartesian xyz space We ll start by calculating the x value The formula is x = r sin f cos q When we plug in the spherical values, we get x = 5 sin (p /2) cos (3p /2) = 5 1 0 = 0 The formula for y is y = r sin f sin q Plugging in the spherical values yields y = 5 sin (p /2) sin (3p /2) = 5 1 1 = 5 The formula for z is z = r cos f When we put in the spherical values, we get z = 5 cos (p /2) = 5 0 = 0 In xyz space, our point can be specified as P = (0, 5,0)
Encoding GS1 - 13 In None
Using Barcode creator for Online Control to generate, create EAN-13 Supplement 5 image in Online applications.
Encoding EAN-13 In VB.NET
Using Barcode generator for .NET Control to generate, create EAN / UCC - 13 image in Visual Studio .NET applications.
Another example Let s convert the xyz space point ( 1, 1,1) to spherical coordinates To find the radius, we use the formula
Bar Code Drawer In .NET
Using Barcode drawer for Reporting Service Control to generate, create barcode image in Reporting Service applications.
EAN / UCC - 13 Maker In None
Using Barcode drawer for Office Word Control to generate, create UCC.EAN - 128 image in Office Word applications.
r = (x2 + y2 + z2)1/2
Spherical Conversions
Plugging in the values, we get r = [( 1)2 + ( 1)2 + 12]1/2 = (1 + 1 + 1)1/2 = 31/2 To find the horizontal angle, we use the formula q = p + Arctan ( y /x) because x < 0 and y < 0 When we plug in the values for x and y, we get q = p + Arctan [ 1/( 1)] = p + Arctan 1 = p + p /4 = 5p /4 To find the vertical angle, we can use the formula f = Arccos (z /r) We already know that r = 31/2, so f = Arccos (1/31/2) = Arccos 3 1/2 Our spherical ordered triple, listing the coordinates in the order P = (q,f,r), is P = [5p /4,(Arccos 3 1/2),31/2]