Question

Can someone walk me through the steps to solve this please?
What is the period of the function?
y = 3 cos pi x

Answer 1

you first need to know what the standard period for cosine is. then we can begin to unfold how they modified it.

Answer 2

is it this? y = a cos(b x)

Answer 3

thats a generic representation of your stated information yes; but that is not the standard period for cosine.

Answer 4

the standard period for cosine is 2pi, in other words: cos(2pi) = cos(0)

pi x = 2pi, when x = 2

so the period is modified in general as: b x ...to.... 2pi/b

Answer 5

now, if we have cos(1/2 x) the period is when 1/2 x = 2pi; x = 4pi

2pi
--- = 4pi
1/2

Answer 6

Okay so I'm a little confused now.

Answer 7

how is 2pi/b confusing?

Answer 8

would the period be just 2pi ?

Answer 9

of course not ... since you stated the general setup at cos(b x) then the period is 2pi/b

2pi/pi = 2

Answer 10

the standard unmodified period of cosine is 2pi .... cos(b x) when b=1

2pi/1 = 2pi