Question

How do you find the amplitude, period and phase shift for `y=1/2sin(theta-pi/2)+4`?

Answer 1

amplitude: `1/2`
period: `2π`
phase shift: shift right `π/2`

Explanation:

First start with the base equation of `y=asin(bx-c)` to find everything, where `a=1/2`, `b=1`, and `c=π/2`.

To find amplitude, the equation is the absolute value of `a`, or `|a|`, meaning that the amplitude is `1/2`.

To find the period, use the equation `(2π)/b`. Plug `1` into b to get `(2π)/1`, so the period is just `2π`.

Finally, for the phase shift, use `bx+c=0`. Plug everything in so that `1Θ-(π/2)=0`. Add `π/2` to both sides to get `Θ=π/2`. This shows that the graph will be shifted `π/2` units to the right, since it is positive.