Help with trig problem please?

Question

I need to use the limit definition which is F'(x)= f(x+h)- f(x)/ h to find the equation of the derivative of f givin that f(x) = sin(x). I know the answer is cos(x), but I do not know how to get there. Thanks

Answer 1

Remember the addition formula for the sin function

sin(a+b) = sin(a)cos(b)+cos(b)sin(a)

F'(x) = sin(x+h)-sin(x) / h

= sin(x)cos(h) - cos(x)sin(h) - sin(x) / h

Limit h -> 0 cos(h) -> 1 and sin(h)/h -> 1

So the eq above becomes sin(x) - sin(x) / h + cos(x)

= cos(x)

Answer 2

http://www.themathpage.com/aCalc/sine.htm

go there, half way down the page. i was writing this out and it was far to hard to try to get all the parenthesis in the right place so i looked online...i went through their reasoning its exactly what i was trying to write. the second step is a trig substitution of sin(v)-sin(u).

if you would like more detail, message me and i will write something otu and e-mail it to you