Expert: Paul Klarreich - 9/20/2007

Question
HI THERE. I am working on graghing sine fuctions and am struggling yet making it work so far. As I work this problem: y=sin4x  - I have determined the period to be pi/2? If this is corect , how do i divide pi/2 by 4 to get my x values?

Answer
Questioner:   MICHAEL
Category:  Advanced Math
Private:  No
 
Subject:  college math - graghs of sine functions
Question:  HI THERE. I am working on graghing sine fuctions and am struggling yet making it work so far. As I work this problem: y=sin4x  - I have determined the period to be pi/2? If this is corect , how do i divide pi/2 by 4 to get my x values?
.....................................
Hi, Michael,

Yes, the period is pi/2.  Set the  'argument' equal to 2pi and solve the equation.  The argument is the object of the sine function, in this case 4x.

Here is my recommendation for graphing a sine or cosine curve:

==== USE COURIER FONT TO VIEW THIS =====

1. If it is a sine curve, draw:


 +   /-\
 | /    \
 |/       \
 0----+----*----+----+
 |          \       /
 |           \    /
 +             \-/

That is a CYCLE.  Now mark the vertical axis with the amplitude in:

y = A sin (nx). In this case, your  A = 1

1+   /-\
 | /    \
 |/       \
 0----+----*----+----+
 |          \       /
 |           \    /
-1+             \-/


Determine the period, as you did:  Set  nx = 2pi  and solve.  In this case, you had the period as  pi/2.  Mark that at the end of the cycle:


1+   /-\
 | /    \
 |/       \
 0----+----*----+----+
 |          \       /pi/2
 |           \    /
-1+             \-/

Take half the period and put it in the middle of the cycle.

1+   /-\
 | /    \
 |/       \
 0----+----*----+----+
 |        pi/4      /pi/2
 |           \    /
-1+             \-/


Take half of THAT and put it as the first quarter of the cycle:

1+   /-\
 | /    \
 |/       \
 0----+----*----+----+
 |  pi/8  pi/4      /pi/2
 |           \    /
-1+             \-/

Take three times THAT and put it as the third quarter of the cycle:

1+   /-\
 | /    \
 |/       \
 0----+----*----+----+
 |  pi/8  pi/4 3pi/8 pi/2
 |           \    /
-1+             \-/


That's your graph.  If you need more of the graph, you will have to extend this cycle to whatever interval is required.