Question

why derivative of sinx is equal to cosx ??plz tell me how to solve derivative and understand the trignometric derivative?

Answer 1

if you take integral of cosx than you find sinx :) there is relationship between differentiation and integral http://en.wikipedia.org/wiki/Derivative

Answer 2

I guess the question is how to prove that derivative of sin is cos; not the formulae as such; may be it can be explained with examples

Answer 3

you can do it with the difference quotient, but you will need a few trig identities, and make use of the fact that\[\lim_{x\to0}\frac{\sin x}{x}=1\]

Answer 4

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-a-definition-and-basic-rules/session-8-limits-of-sine-and-cosine/

Answer 5

A Derivative is nothing more than the slope between two points. It is defined as the limit as delta x approaches zero, followed by Newton's Difference Quotient. Make a graph of sin (x). Now, graph cos (x). Indeed, what you will see is that cos (x) truly is describing the slope of sin (x). So, why do we call it a derivative? Why not? I argue that if we called it "slope", we wouldn't feel like we're all that special. Apparently, mathematicians have a serious inferiority complex. :-) Hope that helps a bit. Also, remember your unit circle; derivatives move clockwise, while anti-derivatives move counter clockwise. Thus, the anti-dervivative of sine (x) is -cos (x). Have fun!

Answer 6

hi woodsmack, apparently decsription you gave to me ...i got it.....i will do it manually ..................thank you

Answer 7

woodsmack's answer is very nice!
do u know the mathematical defenition of the derivative?
I think it is very nice, a nice and beatifull idea, and u can prove q calculate other derivatives with it. like what is the derivative of x^2 ? it isn't much more obvious than sin(x)

good luck! and enjoy :)
p.s u will need some limits like turing test said before