Tangent and Secant Function Applications

In summary: The aysmtope is the part of the graph that is not useful because it represents the point where the graph crosses the y-axis. So if you wanted to find the height of a tree, you would have to use the graph to approximate the height and then take the difference between the approximate value and the true value.
  • #1
TheOmnipotentJuggler
4
0
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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  • #2
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).
 
  • #3
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.
 
  • #4
Given the length of the shadow and the angle to the top of a tree, how tall is the tree?
 
  • #5
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?
 
  • #6
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.
 
  • #7
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.
 
  • #8
That is very helpful, thank you. That is more what I was wondering about.
 

1. What are tangent and secant functions?

Tangent and secant functions are two trigonometric functions that are used to calculate the relationship between the sides and angles of a right triangle. The tangent function is equal to the ratio of the opposite side to the adjacent side, while the secant function is equal to the ratio of the hypotenuse to the adjacent side.

2. How are tangent and secant functions used in real life?

Tangent and secant functions have many real-life applications, such as in engineering, physics, and astronomy. They are used to calculate distances, heights, and angles, and are also used in navigation and surveying.

3. What are some examples of tangent and secant function applications?

Some common examples of tangent and secant function applications include calculating the height of a building or a tree, determining the distance between two objects, and finding the angle of elevation or depression.

4. What is the relationship between tangent and secant functions?

The relationship between tangent and secant functions is that the secant function is the reciprocal of the cosine function, while the tangent function is the reciprocal of the cotangent function. This means that the values of these functions are related, and one can be expressed in terms of the other.

5. How do I solve problems involving tangent and secant functions?

To solve problems involving tangent and secant functions, you can use trigonometric identities, properties, and formulas. You can also use a scientific calculator or a trigonometric table to find the values of these functions for different angles.

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