Question

Select the functions that have identical graphs.

Answer 1

The correct option is:

option: c c. 1 and 3

Explanation:

The first trignometric function is given by:

`y=\sin (3x+(\pi)/(6))`

and also we know that:

`\sin \theta=\cos((\pi)/(2)-\theta)`

This means that:

`\sin (3x+(\pi)/(6))=\cos ((\pi)/(2)-(3x+(\pi)/(6))\\\\\\\sin (3x+(\pi)/(6))=\cos ((\pi)/(2)-3x-(\pi)/(6))\\\\\\\sin (3x+(\pi)/(6))=\cos ((\pi)/(2)-(\pi)/(6)-3x)\\\\\\\sin (3x+(\pi)/(6))=\cos ((2\pi)/(6)-3x)\\\\\\\sin (3x+(\pi)/(6))=\cos ((\pi)/(3)-3x)\\\\\\\sin (3x+(\pi)/(6))=cos (-(3x-(\pi)/(3)))`

As we know that:

`\cos (-\theta)=cos(\theta)`

Hence, we have:

`\sin (3x+(\pi)/(6))=\cos (3x-(\pi)/(3))`

Also, by the graph we may see that the graph of 1 and 2 function do not match.

Hence, they are not equivalent.

Answer 2

c. 1 and 3

Explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot each equation.

Please see the attached image below, to find more information about the graph s

The equations are:

1) y = sin (3x + π/6)

2) y = cos (3x - π/6)

3) y = cos (3x - π/3)

Looking at the graphs, we can see that the identical ones

are equations one and three

Correct option:

c. 1 and 3