How do you graph #y = -3sin (1/2x - pi/4) #?

1 Answer
Kat
Oct 10, 2015

Amplitude=3
Period=4 #pi#
Phase shift= #pi/2#
With reflection about the x-axis.

Explanation:

y=Asin( #omega# x- #phi#)
The (-) before the A indicates a reflection about the x-axis
A is amplitude in absolute value |A|
To find the period for sin you use #2pi/omega#
To find the phase shift you use #Phi/omega#

#2pi#/#1/2# =#4pi#

#pi/4#/#1/2#=#pi/2#

Divide the period by 4 to get the 4 sections of the graph.
#4pi/4#=#pi#

Start your first point on the graph using the phase shift, which is #pi/2# to the right (if the equation was + #pi/4# the shift would be left) . From there, each section is over by #pi# and don't forget the reflection.

You may find it easiest to make each tick mark on the x-axis= #pi/2#.

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