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

  • Thread starter Thread starter Jan Hill
  • Start date Start date
  • Tags Tags
    Inverse Secant
Click For Summary
To solve for y in the equation y = sec^-1(9s^4 + 7), start by expressing the secant function as secy = 9s^4 + 7. The next step involves rearranging the equation to isolate s on one side. If the goal is to find the derivative of y with respect to s, apply the chain rule to differentiate the left-hand side of the equation. Clarifying the specific objective—whether to express s in terms of y or to find the derivative—will guide the next steps in the solution process. Understanding these approaches is essential for effectively tackling the inverse secant problem.
Jan Hill
Messages
63
Reaction score
0

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?
 
Physics news on Phys.org
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:​
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

What is the Derivative of Inverse Secant and its Graph Representation?
  • · Replies 19 ·
Replies
19
Views
6K
Derivative of Secant: Find dy/dx
  • · Replies 2 ·
Replies
2
Views
1K
Derivative of an inverse function
  • · Replies 5 ·
Replies
5
Views
2K
Finding the Slope of Secant and Tangent Lines
  • · Replies 2 ·
Replies
2
Views
2K
Secant Method Minimum Estimation
  • · Replies 3 ·
Replies
3
Views
2K
Inverse of a multivariate function
  • · Replies 12 ·
Replies
12
Views
4K
Slope of Secant Homework: y=x^2+x, P(1,2) & Q(2,6)
  • · Replies 4 ·
Replies
4
Views
2K
Derivative of Inverse Function
  • · Replies 14 ·
Replies
14
Views
2K
Finding the Inverse of 2 (mod 17): Euclidean Extended Algorithm
  • · Replies 6 ·
Replies
6
Views
2K
Proving Injectivity of Shroeder-Berstein Theorem for R to R^2 x R^2
  • · Replies 5 ·
Replies
5
Views
2K