Why is the derivative of a sine function a cosine function?

Question

I'm having a hard time to explain in words why the derivative of a sine function is a cosine function.

Could use some help with this. Read my textbook have been researching the net but haven't got anything yet, I get examples of problems but I still can't put into words.

I appreciate the help.

Answer 1

look at the seerees xpand:

sine(x)=x -(x^3/3!)+(x^5/5!) -(x^7/7!)+...

take derivativ=1-3*x^2/(1*2*3) +...

3x^2 term become x^2/2!

eech part become the seerees for the Kosine:

kosine(x)=1 -(x^2/2!) + (x^4/4!) -...

Answer 2

I need help writing a few sentences telling the reason why the derivative of a sine function a cosine function?

I know slope of the tangent line of sin x is 1 and -1 and so forth, but I am having a hard time explaining in writing the reason why it happens that way.

 

Thank you for the help.