Question

Please, help me out with this

Answer 1

E

Explanation:

As a = 0, cos graph start from its lowest point

Answer 2

Option E

Explanation:

In the equation:

`y = a \cdot \cos(b(x-c)) + d` ...

1) as
`|a|` increases, the wave’s amplitude increases

`A = |a|`

2) as
`b` increases, the wave’s period (wavelength) decreases

`b \propto (1)/(\lambda)`
`\text{period} = (2\pi)/(b)`

3) as
`c` increases, the wave shifts to the right (phase shift)

`c = \text{shift } x`

4) as
`d` increases, the wave shifts upwards (vertical shift)

`d = \text{shift } y`

________________________________________________

We can identify the following information in this problem:

`a = (1)/(2)` → Amplitude is
`(1)/(2)`

`b = 3` → Period is
`(2\pi)/(3)`

`c = (\pi)/(3)` → Phase shift is
`(\pi)/(3)`

`d=0` → Vertical shift is
`0`

So, we can deduce that Option E is correct, as it matches these attributes.

We can differentiate it from Option C by looking at its phase shift, which is is half of the period length, so it will appear as though it has a negative amplitude.