How do you write an equation of a sine function with amplitude 0.5, period 4pi, phase shift pi/6 to the left, vertical displacement 1 unit up?

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Answer 1 · 2018-01-02T19:59:37

#y=1/2sin(1/2x+pi/12)+1#

We can express trig function in the following way:

#y=asin(bx+c)+d#

Where:

Amplitude = a.

Period #=(2pi)/b#. ( #2pi# is the normal period of sin(x) )

Phase shift #=-c/b#.

Vertical shift #= d#.

For our example:

#a=1/2#

Period needs to be #(4pi)#

#:.#

#(2pi)/b=4pi=>b=1/2#

Phase shift needs to be #pi/6#

#:,#

#-c/(1/2)=pi/6=>c=-pi/12# ( this is #pi/12# for shift to the left )

Vertical shift needs to be 1

#d=1#

So our equation is:

#y=1/2sin(1/2x+pi/12)+1#