Hyperbolic and Inverse Functions

[GRB 080319B]

Hyperbolic and Inverse Trigonometric Functions

How extensive is the use of hyperbolic and inverse trigonometric functions in upper-level calculus and mathematics? I've taken 3 semesters of calculus, and not one of my teachers has gone over hyperbolic functions, and barely touched on inverse trig functions (no calculus involved). I've never encountered any problems dealing with hyperbolic or inverse trig functions in any of the tests or quizzes I've received (including the AP test for AP Calculus AB). I've seen chapters devoted to these subjects in my books, but have never covered the material or been tested on the material in class (and thus never studied them). I'm wondering if these are truly arcane subjects that my teachers decided to sweep under the rug due to time constraints, or are truly important in more advanced classes.

Thank you.

 

[Tac-Tics]

How extensive is the use of hyperbolic and inverse functions in upper-level calculus and mathematics?

Are you talking about hyperbolic and inverse TRIGONOMETRIC functions?

Inverse sine, cosine, and tangent are used all the time. For example, to find the angle between two vectors, you need to take the inverse cosine of their dot product divided by the product of their lengths.

I never formally learned about hyperbolic trig functions, but they do have their applications. In particular, they are used in the formulation of special relativity. A lorentz transformation is either a rotation between two spatial dimension or a hyperbolic rotation between one spatial dimension and time (or some combination thereof).

 

[Ben Niehoff]

Hyperbolic functions are used a lot in physics, particularly in solving differential equations. They have properties that are very similar to trigonometric functions, but with some sign changes. So sometimes they are easier to work with than exponentials.

 

[g_edgar]

Hmmm ... maybe the math department has specialists in algebra and number theory teaching freshman calculus. Since they never use hyperbolic functions, they think it is safe to skip that material to save time.

 

[GRB 080319B]

Are you talking about hyperbolic and inverse TRIGONOMETRIC functions?

I apologize for omitting the trigonometric part; that is what I meant. I have used inverse trig functions for the angles between two vectors, but that was the terminus. I was inquiring as to the calculus applications, because in the back of the books I've used are numerous derivatives and integrals which use hyperbolic and inverse trig functions, and I have yet to utilize them. I understand now that they have applications in physics and differential equations.

Thank you for your replies.