Sin(x) takes more parameters

You may be aware that I have approximate expressions for factorial,  to the power n and the next number. 

So I tried on Wolfram Alpha using above.

I always thought where there is cos(x) , there is sin(x). And they have same number of parameters.

But not so.

The above happens at only one place. At x = 4 or x=1/4 depending on whether x^n is in numerator or denominator.

Have a nice day!! May God bless us !!