Microsoft KB Archive/11158

PRB: tan(pi/2) Returns Value, Causes No Error Article ID: Q11158 The information in this article applies to: The C Run-time (CRT), included with: - Microsoft C for MS-DOS, versions 5.1, 6.0, 6.0a, 6.0ax - Microsoft C for OS/2, versions 5.1, 6.0, 6.0a - Microsoft C/C++ for MS-DOS, version 7.0 - Microsoft Visual C++ for Windows, versions 1.0, 1.5 - Microsoft Visual C++ 32-bit Edition, versions 1.0, 2.0, 4.0, 5.0 SYMPTOMS If an application uses the tan() run-time function to compute the value of pi/2, the function returns a value. Mathematically, this value is not defined. CAUSE This error is caused by the precision with which numbers can be represented in the computer. It is not possible to specify a value X close enough to the true value of pi/2 to cause tan(X) to overflow. MORE INFORMATION The tangent of a value is defined as the sine of the value divided by the cosine of the value. Therefore, the tangent of pi/2 is the sine of pi/2 (1) divided by the cosine of pi/2 (0). Because the cosine of pi/2 is 0, its tangent is undefined. sin(pi/2) 1 tan(pi/2) = ----------- = --- = undefined, divide by zero cos(pi/2) 0 The function tan(pi/2) returns a value because the computer approximates pi to a limited number of digits. Even at double precision, the approximate value of pi is not large enough to cause cos(pi/2) to equal zero. Therefore, tan(pi/2) returns an unexpected value, as follows: Approximate pi = 3.1415926535 sin(pi/2) sin(3.1415926535/2) 1 tan(pi/2) = ----------- = ------------------- = ----------------- cos(pi/2) cos(3.1415926535/2) 0.000000000044896 Keywords  : kbCRT kbVC Version  : 5.1 6.0 6.0a 6.0ax 7.0 1.0 1.5 2 Platform  : MS-DOS NT OS/2 WINDOWS Issue type  : kbprb

Last Reviewed: July 27, 1997 © 1999 Microsoft Corporation. All rights reserved. Terms of Use.