Derivatives of trigonometric functions

AI Thread Summary
The discussion focuses on understanding the derivatives of trigonometric functions, specifically the derivative of sine. The user is exploring the formula for the sine of a sum, sin(A + B) = sinAcosB + sinBcosA, to clarify their confusion about the cosine term in the equation. They initially struggled with the concept but realized that the formula applies to sin(x + ΔY) as well. This realization helped them grasp the relationship between sine and cosine in derivatives. The conversation highlights the importance of foundational trigonometric identities in understanding calculus concepts.
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Homework Statement


I'm learning now about darivative all by my self (without a teacher) and I'm not sure about this development

Homework Equations







The Attempt at a Solution



Y=senx

y+{\Delta}Y=sen(x+{\Delta}Y)

{\Delta}Y=senx*cos{\Delta}x+ sen{\Delta}x*cosx

What about this cos,what is it doing in the equation?
I really don't get it.
 
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this comes from the double angle formula.

it says that: sin (A + B) = sinAcosB + sinBcosA

you can find the same thing for sin (x + dY)
 


Oh,now I think i get it!
Thankyou!
 

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