Find Inverse of A w/ Trig Functions: Step-by-Step Guide

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In summary, the conversation is about finding the inverse of a matrix A that involves long trigonometric functions. The person is unsure how to proceed and asks for guidance. They are given the option to use the transposed cofactor matrix method and advised to check for values of \theta and \phi that may make the matrix non-invertible.
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Reshma
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Find the inverse of A given by:
[tex]A = \left[\begin{array}{ccc}\cos \phi & -\cos \theta \sin \phi & \sin \theta \sin \phi \\\sin \phi & \cos \theta \cos \phi & -\sin \theta \cos \phi \\0 & \sin \theta & \cos \theta\end{array}\right][/tex]

I have never encountered a problem in Matrices involving long trigonometric functions. How do I find the inverse? Should I use the same row-reduction method for this?
 
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  • #2
Use whatever method you prefer (I like the transposed cofactor matrix method, personally). Once you specify [itex]\theta, \ \phi[/itex], they're just numbers (you should, of course, check to make sure that there are no values of these that stop the matrix from being invertible!).
 
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Ok, thanks a lot! I will try it out.
 

FAQ: Find Inverse of A w/ Trig Functions: Step-by-Step Guide

What is an inverse function?

An inverse function is a function that undoes the action of another function. In other words, if a function f(x) takes a number x and produces a result y, then the inverse function f^-1(y) will take the result y and produce the original number x.

Why is it important to find the inverse of a function?

Finding the inverse of a function is important because it allows us to solve equations and simplify expressions that involve the original function. It also helps us to understand and analyze the behavior of the original function.

How do you find the inverse of a function using trigonometric functions?

To find the inverse of a function that includes trigonometric functions, you first need to isolate the trigonometric function on one side of the equation. Then, use the inverse trigonometric function (such as sin^-1, cos^-1, or tan^-1) to solve for the variable. Finally, switch the roles of the variable and the result to get the inverse function.

What are the key steps in finding the inverse of a function?

The key steps in finding the inverse of a function are:

  • Isolate the trigonometric function on one side of the equation.
  • Use the inverse trigonometric function to solve for the variable.
  • Switch the roles of the variable and the result to get the inverse function.

Are there any restrictions when finding the inverse of a function with trigonometric functions?

Yes, there are some restrictions when finding the inverse of a function with trigonometric functions. These include:

  • Some trigonometric functions have multiple values for a given input, so the inverse function may not be a true inverse in these cases.
  • The domain and range of the original function may need to be restricted in order for the inverse function to exist.
  • Some trigonometric functions are not one-to-one, meaning they do not have an inverse function.

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