Question

How do you find the amplitude, period, vertical and phase shift and graph `y=sintheta+0.25`?

Answer 1

Below

Explanation:

`y=sintheta+0.25` can also be written as `y=0.25+sintheta` which is in the form `y=b+asin(ntheta)`
where `a` is the amplitude and `b` is the shift upwards or downwards and `n` is the phase shift

Now when we compared `y=0.25+sintheta` and `y=b+asin(ntheta)`, we can say that:

`b=0.25`
`a=1`
`period(T)=(2pi)/n=(2pi)/1=2pi`

Therefore, we know that `y=sintheta+0.25` is the graph `y=sintheta` shifted UPWARDS by `0.25` units and they also have the same phase shift `(2pi)`

Below is graph `y=sintheta`

graph{sinx [-10, 10, -5, 5]}

Below is graph `y=sintheta+0.25`

graph{0.25+sinx [-10, 10, -5, 5]}