Tangent and Secant Function Applications

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Homework Help Overview

The discussion revolves around the applications of the tangent and secant functions, particularly in real-world contexts. The original poster expresses difficulty in identifying practical uses for these functions, especially in relation to their graphical representations and characteristics such as vertical asymptotes.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between the tangent function and real-life scenarios, such as calculating heights using angles and shadows. There is a focus on understanding how the tangent graph relates to these applications. Some participants question the validity of using the tangent graph in specific contexts.

Discussion Status

The discussion is ongoing, with participants providing insights and examples related to the tangent function. There is a mix of interpretations regarding the application of the tangent graph, and some guidance has been offered regarding its use in approximations, though no consensus has been reached.

Contextual Notes

Participants are navigating the challenge of connecting mathematical concepts to practical problems, with some expressing confusion over the distinction between the tangent function's graphical representation and its trigonometric definition. The presence of vertical asymptotes in the tangent function is also a point of discussion.

TheOmnipotentJuggler
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Hello all, I have a question concerning the Tangent and Secant Functions (the graphs). I cannot think of a way that either of these can be used in the real world. I need to find applications for these. For example, the sine function can be used to represent waves or periodic motion... but what can secant and tangent represent? I have been thinking about this for a very long time and I cannot seem to find an answer. The difficult thing about the Tangent function is that it has a vertical asymptote? What things in today's world could use asymptotes, and then repeat? The Secant, that is just weird looking and seems in no way possible to fit a model of data? Please help me, I cannot figure it out. Thank you. :eek:
 
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the tangent of the angle formed by a line and the x-axis is equal to the slope.

secant is useful for calculating the derivative of tangent (ok, that one's cheating).
 
I meant more like story problems. Unless that answer was a story problem... I'm sorry I guess I don't understand your answer. I am looking for some sort of real-life problem that could come up and eventually use the tangent function to solve it. Thank you.
 
Given the length of the shadow and the angle to the top of a tree, how tall is the tree?
 
Thank you, but that is not the tangent function as in the graph. That is like tan=sin/cos stuff. You cannot use the tangent graph to find the height of a tree can you?
 
TheOmnipotentJuggler said:
Thank you, but that is not the tangent function as in the graph. That is like tan=sin/cos stuff. You cannot use the tangent graph to find the height of a tree can you?
As a matter of fact you can. It will of course be an approximation.
 
TheOmnipotentJuggler said:
Thank you, but that is not the tangent function as in the graph. That is like tan=sin/cos stuff. You cannot use the tangent graph to find the height of a tree can you?

It is one and the same. I guess I do not know what you want to do with the graph. The graph is simply a display of the values of the Tan function.

Consider what happens to the shadow if the sun were to be exactly above the tree. The height of the tree would not matter, the length of the shadow would be zero. There is the aysmtope which appears at 90deg in the graph.
 
That is very helpful, thank you. That is more what I was wondering about.
 

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