Understanding the change from cot graph to tan graph

[Niaboc67]

Homework Statement

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

 

[Mark44]

Homework Statement

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.

 

[RUber]

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.