Question

Graph function 1/2y=sin(3x+180)

Answer 1

Graph is shown below

Explanation:

We have the function,
`(1)/(2)y=sin(3x+180)`

That is,
`y=2sin(3x+180)`

We see that,

If a function f(x) has period P, then cf(bx) will have period
`(P)/(|b|)`.

Since, the
`y=\sin x` has period
`2\pi`, then the given function have period
`(2\pi)/(3)`.

The given sine function has period
`(2\pi)/(3)` and amplitude 2.

Hence, the graph of the function is shown below.

Answer 2

The graph of the given function is shown below.

Explanation:

The given function is

`(1)/(2)y=\sin (3x+180)`

Multiply both sides by 2.

`y=2\sin (3x+180)` ....(1)

The general form of sine function is

`f(x)=a\sin(bx+c)+d` ....(2)

Where, a is altitude, b is period, c is phase shift and d is vertical shift.

On comparing (1) and (2), we get

`a=2,b=3,c=180`

it means the altitude of the function is 2, period is 3 and phase shift is 180.

The graph of the given function is shown below.