Solving Inverse Secant Problem: Finding y = sec^-1(9s^4 + 7)

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SUMMARY

The discussion focuses on solving the inverse secant problem, specifically finding the value of y = sec^-1(9s^4 + 7) with respect to the variable s. The initial equation secy = 9s^4 + 7 is established, prompting participants to explore rearranging the equation to isolate s. Additionally, there is a suggestion to differentiate y with respect to s using the chain rule, indicating a dual approach of solving for s and finding the derivative.

PREREQUISITES
  • Understanding of inverse trigonometric functions, specifically secant.
  • Familiarity with algebraic manipulation and rearranging equations.
  • Knowledge of differentiation techniques, particularly the chain rule.
  • Basic understanding of calculus concepts related to derivatives.
NEXT STEPS
  • Study the properties of inverse secant functions and their applications.
  • Learn how to rearrange equations to isolate variables effectively.
  • Explore differentiation techniques, focusing on the chain rule in calculus.
  • Practice solving similar problems involving inverse trigonometric functions.
USEFUL FOR

Students studying calculus, particularly those focusing on trigonometric functions and their inverses, as well as educators looking for examples of inverse secant problems.

Jan Hill
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Homework Statement



Find the value of y = sec^-1(9s^4 + 7) with respect to s

Homework Equations






The Attempt at a Solution



secy = 9s^4 + 7

but where do I go from here?
 
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Hi Jan! :smile:

(try using the X2 icon just above the Reply box :wink:)

Are you trying to find s in terms of y?

Then continue by rearranging your final equation, putting s on the left. :smile:

EDIT: ohhh! … are you trying to find the derivative of y with respect to s?

then differentiate your final equation, using the chain rule for the LHS. :smile:​
 

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