Understanding the change from cot graph to tan graph

In summary, the conversation is discussing the function y = a cot k(x-b) and y = a tan k(x-b), where a, b, and k are coefficients that represent transformations of the graph of y = cot(x). The user is unsure of the values of a, b, and k in the given equations and is advised to experiment with a plotting tool to better understand their roles.
  • #1
Niaboc67
249
3

Homework Statement


ygkRmPW.png


Suppose the function is y = a cot k(x−b)

Then (give exact answers; you can type pi for π):
a =
b =
k =

Suppose the function is y = a tan k(x−b), where b > 0.

Then:
a =
b =
k =

The Attempt at a Solution


Then (give exact answers; you can type pi for π):
a = 4 because this is the amplitude?
b = 2 because this is the period?
k = not sure?

the next section I am at lost at
 
Physics news on Phys.org
  • #2
Niaboc67 said:

Homework Statement


ygkRmPW.png


Suppose the function is y = a cot k(x−b)

Then (give exact answers; you can type pi for π):
a =
b =
k =

Suppose the function is y = a tan k(x−b), where b > 0.

Then:
a =
b =
k =

The Attempt at a Solution


Then (give exact answers; you can type pi for π):
a = 4 because this is the amplitude?
b = 2 because this is the period?
k = not sure?

the next section I am at lost at
Do you know what the graph of y = cot(x) looks like? All of the numbers a, k, and b represent some kind of transformation that has been done to the graph of y = cot(x) to get the one in the drawing. Presumably you have been studying these kinds of transformations already.

Regarding your answers, amplitude doesn't apply in this graph. The period is not 2. You can look at the graph and see what the period is.
 
  • #3
a will amplify the height of the function, so look for what would normally be 1 and see what it is in the graph-- that should be a.
b is a shift.
And k will change the period.
Play around with these and a plotting tool. They will help you understand the role of these coefficients in other expressions.
 

1. What is the difference between a cot graph and a tan graph?

Both cot and tan graphs represent trigonometric functions, but they are different in the way they are calculated. Cotangent (cot) is the ratio of the adjacent side to the opposite side of a right triangle, while tangent (tan) is the ratio of the opposite side to the adjacent side. This means that the values on the y-axis for cot graphs will be the reciprocal of the values on the y-axis for tan graphs.

2. Why do cot and tan graphs have different shapes?

The shape of a graph depends on the values of the function being plotted. Since cot and tan functions are calculated differently, their values will be different, resulting in different shapes of their respective graphs. Cot graphs have a periodicity of pi, while tan graphs have a periodicity of pi/2, which also contributes to their different shapes.

3. How can I convert a cot graph to a tan graph?

To convert a cot graph to a tan graph, you can use the reciprocal property of trigonometric functions. This means that you need to take the reciprocal of the values on the y-axis of the cot graph to get the corresponding values on the y-axis of the tan graph. For example, if the value on the y-axis of the cot graph is 2, the corresponding value on the y-axis of the tan graph will be 1/2.

4. Can I use the same x-axis for both cot and tan graphs?

Yes, you can use the same x-axis for both cot and tan graphs since they represent different trigonometric functions. However, the values on the y-axis will be different, so it is important to label the y-axis accordingly for each graph.

5. What is the practical application of understanding the change from cot graph to tan graph?

Trigonometric functions, including cot and tan, are used to model various phenomena in science, engineering, and mathematics. Understanding the change from cot graph to tan graph can help in solving real-world problems involving trigonometric functions and making accurate predictions based on data represented in graphs.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
17
Views
2K
  • Precalculus Mathematics Homework Help
Replies
15
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
933
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
11
Views
318
  • Precalculus Mathematics Homework Help
Replies
6
Views
2K
  • Precalculus Mathematics Homework Help
Replies
7
Views
3K
  • Precalculus Mathematics Homework Help
Replies
8
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
871
Back
Top