Derivatives of trigonometric functions

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SUMMARY

The discussion focuses on the derivatives of trigonometric functions, specifically the derivative of the sine function, Y = sin(x). The user explores the equation Y + ΔY = sin(x + ΔY) and seeks clarification on the presence of the cosine term in the expansion. The conversation highlights the application of the sine addition formula, sin(A + B) = sinAcosB + sinBcosA, to derive the relationship between sine and cosine in the context of derivatives.

PREREQUISITES
  • Understanding of basic calculus concepts, specifically derivatives.
  • Familiarity with trigonometric functions, particularly sine and cosine.
  • Knowledge of the sine addition formula.
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Study the derivative of cosine functions and their applications.
  • Learn about the chain rule in calculus for more complex derivatives.
  • Explore the unit circle and its relationship to trigonometric functions.
  • Investigate higher-order derivatives of trigonometric functions.
USEFUL FOR

Students learning calculus, particularly those studying derivatives of trigonometric functions, and self-learners seeking to deepen their understanding of mathematical 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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