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.

).

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