Intrinsic Equation: Showing tan φ/2 = e^s

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SUMMARY

The discussion centers on demonstrating the relationship between the intrinsic equation of a curve defined by sin(y) = e^x and the expression tan(φ/2) = e^s, where s is measured from the point (0, π/2). Participants seek clarification on how the variables s and φ relate to x and y within this context. The equation is crucial for solving specific problems in calculus and differential equations, particularly in relation to intrinsic geometry.

PREREQUISITES
  • Understanding of intrinsic equations in calculus
  • Familiarity with trigonometric identities, specifically tan(φ/2)
  • Knowledge of exponential functions and their properties
  • Basic concepts of differential equations
NEXT STEPS
  • Study the derivation of intrinsic equations in calculus
  • Learn about the relationship between trigonometric functions and exponential functions
  • Explore the applications of intrinsic geometry in differential equations
  • Review examples of curves defined by exponential functions and their properties
USEFUL FOR

Students studying calculus, particularly those preparing for exams involving intrinsic equations and differential geometry, as well as educators seeking to clarify these concepts.

kingOFleo
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For the curve with equation siny =e^x, where s is measured from the point(0,pi/2),show that e^s =tan?/2.
tan?/2 where?=phi
hlp me please
contact me nikvoodoo@gmail.com
 
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You definitely haven't given enough information... how are s and phi related to y and x?
 
i also can't understand this but this came in my exam
please try to this
hlp me
 

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