In this blog post, we explore incorrect calculations of the secant function sec(x) and cosecant function csc(x) for large numbers in MATLAB.
Example 1. Given that x = 1234567890888777.123, calculate sec(x) and csc(x).
Using MATLAB, I computed the values of sec(x) and csc(x) at x = 1234567890888777.123. The result is shown in the following screenshot.
From the above screenshot, it can be seen that the outputs from MATLAB are and respectively.
However, the correct values with 16 significant digits are -0.1116013690832344e1 and -0.2252452617594792e1, respectively (as provided by ISRealsoft).
Therefore, out of the 32 significant digits in the two outputs from MATLAB, only 1 digit is correct. The error rates are 15/16 = 93.75% and 16/16 = 100%, respectively.
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