Im not sure if its the right place to ask this question since it may be more of an informatics problem and I apologize if its the case:
I want to evaluate a certain function, $\frac{log(cos(x))}{x}$ on the interval $[0;10^{-7}]$
,
I know that the function is equivalent to $\frac{1}{2x}log(1-sin^{2}(x))$ but when I draw them on matlab, on this interval, I get this
The red line is the $\frac{1}{2x}log(1-sin^{2}(x))$ form of the function, the blue line the $\frac{log(cos(x))}{x}$ form.
How can one explain this, do I have one form more well-conditionned than the other? Is it a stability problem?