Question

Select the graph of y= 2 cos (4x) +1.TOTITC

Answer 1

Given the equation:

`y=2\cos (4x)+1`

Let's graph the equation.

Apply the form:

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

Where:

a = 2

b = 4

c = 0

d = 1

Let's determine the amplitude, period, phase shift and vertical shif.

Amplitutde = a = 2

To find the period, we have:

`(2\pi)/(b)=(2\pi)/(4)=(\pi)/(2)`

Phase shift:

`(c)/(b)=(0)/(4)=0`

Vertical shift, d = 1

Find few points of the equation on a graph.

We have:

When x = 0

y = 2 cos (4(0))+1

y = 2 cos (0)+1

y = 2 (1) + 1

y = 2 + 1

y = 3

When x = π/8

y = 2 cos (4(π/8)) + 1

y = 2 cos(π/2) + 1

y = 2 (0) + 1

y = 0 + 1

y = 1

When x = π/4

y = 2 cos(4(π/4))+1

y = 2 cos(π) + 1

y = 2 (-cos(0)) + 1

y = 2(-1) + 1

y = -2 + 1

y = -1

WHen x = π/2

y = 2 cos(4(π/2)) + 1

y = 2 cos(2π) + 1

y = 2 cos(0) + 1

y = 2(1) + 1

y = 2 + 1

y = 3 =

Thus, we have the points:

(0, 3), (π/8, 1), (π/4, -1), (π/2, 3)

The graph of the equation is attached below: