Finding the Normal Equation for a Curve at a Given Point

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SUMMARY

The discussion focuses on finding the normal equation for the curve defined by the equation 2y + sin(x) = x * cos(y) at the point (0,0). The derivative calculated is (cos(y) - cos(x)) / (2 + x * sin(y)), leading to a tangent slope of 0. Consequently, the slope of the normal line is determined to be undefined, resulting in the normal equation x = 0.

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  • Understanding of implicit differentiation
  • Knowledge of normal and tangent lines in calculus
  • Familiarity with trigonometric functions and their derivatives
  • Basic skills in solving equations involving multiple variables
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  • Study implicit differentiation techniques in calculus
  • Learn about the properties of normal and tangent lines
  • Explore trigonometric derivatives and their applications
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koolkris623
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Find the equation of the line normal to the curve at (0,0). (Normal lines are perpendicular to the tangent lines)

2y + sinx = xcoxy

I found the derivative to be (cosy - cosx)/ (2+ xsiny)

then the slope tangent is 0...then the slope perpendicular to it is undefined...so then is the normal equation..x=0?
 
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That looks ok to me.
 

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