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

Jun 4, 2017

amplitude: $\frac{1}{2}$
period: 2π
phase shift: shift right π/2

#### Explanation:

First start with the base equation of $y = a \sin \left(b x - c\right)$ to find everything, where $a = \frac{1}{2}$, $b = 1$, and c=π/2.

To find amplitude, the equation is the absolute value of $a$, or $| a |$, meaning that the amplitude is $\frac{1}{2}$.

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 $b x + c = 0$. 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.