Question

The graph of which trigonometric function(s) include the point (0,3). Select three of the following that apply.

Answer 1

`y=3\cos(x)`

`y=\sin(2x)+3`

`y=\tan(x)+3`

Explanation:

For
`y=cosx +3`, when
`x=0`,
`y=\cos(0)+3\Rightarrow y=1+3=4`

The graph of this function contains the point
`(0,4)`

For
`y=3\cos(x)`, when
`x=0`,
`y=3\cos(0) \Rightarrow y=3(1)=3`

The graph of this function contains the point
`(0,3)`

For
`y=\sin(2x)+3`, when
`x=0`,
`y=\sin(2(0))+3=3`

The graph of this function contains the point
`(0,3)`

For
`y=\tan(x)+3`, when
`x=0`,
`y=\tan(0)+3=0+3=3`

The graph of this function contains the point
`(0,3)`

For
`y=\sin(3x+(\pi)/(2))+1`, when
`x=0`,
`y=\sin(3(0)+(\pi)/(2))+1`

`\Rightarrow y=\sin(0+(\pi)/(2))+1`

`\Rightarrow y=\sin((\pi)/(2))+1`

`\Rightarrow y=1+1=2`

The graph of this function contains the point
`(0,2)`