may i get some help

Question

to sketch one period of the graph of y=3cos(2xπ/2), we need to compute the function at the following numbers of x:

 

 

Answer 1

y = 3 cos(2 x pi/2) = 3 cos(x pi)

 

If x pi = θ, then y = 3 cos(θ) which has a period 0 ≤ θ < 2 pi.

 

0 ≤ (x pi) < 2 pi

 

0 ≤ x < 2

 

So the length of one period of y = 3 cos(2 x pi/2) is 2-0 = 2.

 

We normally use x values at the beginning and end of a period, and at the 3 quarters in between:

 

x = 0

x = 1/2

x = 1

x = 3/2

x = 2