Graph of trigonometric functions

[ItsAnshumaan]

This is not a homework question but a general doubt.

Suppose we have a function y = pcosx, where 'p' is an arbitrary constant. So my question is how will the graph of this function change with different values of 'p'?

This doubt can also be extended for other functions like y = pe^x, y = p sin^-1x etc, if the concept remains same.

 

[SammyS]

This is not a homework question but a general doubt.

Suppose we have a function y = pcosx, where 'p' is an arbitrary constant. So my question is how will the graph of this function change with different values of 'p'?

This doubt can also be extended for other functions like y = pe^x, y = p sin^-1x etc, if the concept remains same.

Even though you say it's not a Homework problem, you should use the Homework template when you post in a Homework Forum.

At any rate:
What do you think is the effect on the graph, y = cos(x), if you multiply the cosine function by a constant, p, giving the resulting graph y = p⋅cos(x) ?

It may help to pick some value for p, such as p = 2 .

 

[ItsAnshumaan]

Even though you say it's not a Homework problem, you should use the Homework template when you post in a Homework Forum.

At any rate:
What do you think is the effect on the graph, y = cos(x), if you multiply the cosine function by a constant, p, giving the resulting graph y = p⋅cos(x) ?

It may help to pick some value for p, such as p = 2 .

When p is 2, the y co-ordinate will be double of what it should had been in normal cosine graph. Hence I'm assuming that the amplitude of the wave will increase.

 

[member 587159]

When p is 2, the y co-ordinate will be double of what it should had been in normal cosine graph. Hence I'm assuming that the amplitude of the wave will increase.

You are right. More generally, the cosine values has values in [-1,1] . When you consider the function f(x) = p*cos(x), f(x) has values in [-p,p].
Concerning other functions. Generally, when you have a function g(x), then p*g(x) will be the function where for every a in the domain of g, g(a) is multiplied with p.

 

[ItsAnshumaan]

You are right. More generally, the cosine values has values in [-1,1] . When you consider the function f(x) = p*cos(x), f(x) has values in [-p,p].
Concerning other functions. Generally, when you have a function g(x), then p*g(x) will be the function where for every a in the domain of g, g(a) is multiplied with p.

Thank you for the help :D