Sorry I dont know how to type out the equations properly but the links will show each .

How would the derivative of the infinite series of sinx be related to the infinate series of cosx ?

How is negative sinx equivalent to the derivative of the infinite series of cos x?

sinx Sine Definition as an Infinite Series - Calculus - EquationSheet.com

Cos Cosine Definition as an Infinite Series - Calculus - EquationSheet.com

thanks a bunch .