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

1 Answer
Jun 4, 2017

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.