- #1
Jan Hill
- 63
- 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?
Solving Inverse Secant Problem: Finding y = sec^-1(9s^4 + 7)
In summary, the inverse secant problem is a mathematical problem that involves finding the angle whose secant value is a given number. The symbol for inverse secant is sec^-1 or arcsec, and its domain and range are all real numbers between -1 and 1 (excluding -1 and 1) and all angles between 0 and π radians (0 to 180 degrees), respectively. The problem is solved by finding the corresponding angle using a calculator or trigonometric tables and then verifying the answer by plugging it back into the secant function. Inverse secant has various real-life applications, such as in navigation, surveying, physics, engineering, and computer graphics.
Find the value of y = sec^-1(9s^4 + 7) with respect to s
secy = 9s^4 + 7
but where do I go from here?
- #2
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
Hi Jan! 
(try using the X2 icon just above the Reply box)
Are you trying to find s in terms of y?
Then continue by rearranging your final equation, putting s on the left.
(try using the X2 icon just above the Reply box
)Are you trying to find s in terms of y?
Then continue by rearranging your final equation, putting s on the left.
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.
then differentiate your final equation, using the chain rule for the LHS.
What is the inverse secant problem?
The inverse secant problem is a mathematical problem that involves finding the angle whose secant value is a given number. In other words, given a value for the secant of an angle, the inverse secant problem asks us to find the measure of the angle itself.
What is the symbol for inverse secant?
The symbol for inverse secant is sec-1 or arcsec. This is the inverse function of the secant function, denoted as sec(x).
What is the domain and range of inverse secant?
The domain of inverse secant is all real numbers between -1 and 1, excluding -1 and 1. The range of inverse secant is the set of all angles between 0 and π radians (0 to 180 degrees).
How is the inverse secant problem solved?
The inverse secant problem is solved by first taking the given secant value and finding the corresponding angle using a calculator or trigonometric tables. Then, the answer is verified by plugging the angle back into the secant function to ensure that the result is equal to the given value.
What are some real-life applications of inverse secant?
Inverse secant is commonly used in navigation and surveying, as well as in physics and engineering problems involving angles and angular measurements. It is also used in computer graphics and animation to calculate the angle of rotation needed to create a specific curve or shape.
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