Question

Which function's graph has a period of 2?

A. y=cos(x-pi/2)
B. y=3cos pi x
C. y=2 sin 3x
D. y=-4 sin 2x

Answer 1

B is correct.

Function y=3cos(πx) would be period 2.

Explanation:

We are given a trigonometric equation. We need to find the function whose period is 2.

`y=a\cos(bx+c)`

Where,

a is amplitude of function.

b is wavelength of function.

c is phase shift of function.

As we know the period of y=cos x is 2π

So, Period of function, y=cos(ax) would be
`(2\pi)/(a)`

If we divide 2π by coefficient of x we get period of function.

We are given period is 2

`\text{Coefficient of x}=(2\pi)/(2)`

`\text{Coefficient of x}=\pi`

Thus, B is correct. Function y=3cos(πx) would be period 2.

Answer 2

Given that the function is:

y=a cos( bx+c), or y=a sin(x+c)

then the period is calculated as T= 2π/b and if T=2:

2=2π/b
b=2π/2=π

Therefore, the correct answer is option B, y=3 cos πx.

Hope this answers the question. Have a nice day.