PRB: tan(pi/2) Returns Value, Causes No Error

 Last reviewed: July 25, 1997
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          : CRTIss kbfasttip
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

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Last reviewed: July 25, 1997
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