Incorrect calculations by the computer: tan(x) and cot(x) for large values of x

In this blog post, we explore incorrect calculations of the tangent function tan(x) and the cotangent function cot(x) for large numbers in MATLAB.

Example 1. Suppose $x=235556677777.87\,.$ Calculate $\tan(x)$ and $\cot(x)$ in MATLAB.

Let's just post the figure directly.

From the above figure, it can be seen that the two outputs from MATLAB are
$1.4290\red{64236906033}$ and $0.69975\red{8607188316} .$

However, the correct values with 16 significant digits are 0.1429079091621959e1 and 0.6997513334724058, respectively (as provided by ISRealsoft).

As a result, both outputs from MATLAB contain 11 incorrect digits, with an error rate of 11/16 = 68.75% for the significant figures.