How do you graph #f(x)=2 sin(x/3)#?

1 Answer
Ernest Z.
Aug 11, 2015

Plot the maxima, minima, and intercepts over one period, then extend the graph in each direction.

Explanation:

Your equation is #f(x) =2sin(x/3)#

Step 1. Express your equation in the form

#f(x)=asin(bx+c)+d#

Then #a=2#, #b=1/3#, #c=0#, and #d=0#.

Step 2. Calculate the range, period, phase shift, and vertical displacement.

The amplitude is #a = 2#, so the range is [-2,2].

The period is #(2π)/b = (2π)/(1/3) = 6π#.

The phase shift is #c=0#.

The vertical shift is #d=0#.

Step 3. Divide the period #6π# into four quarters to get the key points for #f(x) = 2sin(x/3)#.

#stackrel(—————————————————————)(x=" "" "0" "(3π)/2" "color(white)(1)3π" "(9π)/2" "6π)#
#stackrel(—————————————————————)(f(x)=color(white)(1)0" "color(white)(1)2" "" "0" "-2" "0)#
#stackrel(—————————————————————)#

These points are

  • (#0,0#) = intercept
  • (#(3π)/2,2#) = maximum
  • (#3π,0#) = intercept
  • (#(9π)/2,-2#) = minimum
  • (#6π,0#) = intercept

Step 4. Plot these five key points.

Graph1

Step 5. Join these points with a smooth curve.

Graph 2

Step 6. Follow the pattern and extend your axis from #-6π# to #12π#.

Graph 3

And you have your graph.

Related questions
See all questions in General Sinusoidal Graphs
Impact of this question
3063 views around the world
You can reuse this answer
Creative Commons License