IMAP^2 Fairfield , IA
Trig Function Explorations
June 2008 Notes by WS
EXAMPLE 1
Ÿ The graphic below shows the two curves
y1 = Sin[x] and
y2= (1/3) Sin [ 3 x ]
x Î[-2Π, 2Π], y Î[-3,3 ].
QUESTION: what does the curve y1 + y2 look like? See next cell for an answer.
Plot@8Sin@xD, H1  3L Sin@3 * xD<, 8x, -2 Pi, 2 Pi<,
PlotRange ® 8-3, 3<, PlotStyle ® [email protected]<, ImageSize ® 600D
3
2
1
-6
-4
-2
2
-1
-2
-3
4
6
2
Two-Three-FourierTerms-061708-22.nb
Ÿ y1 = Sin[x] and
y2 = (1/3) Sin [ 3 x ]
x Î[-2Π, 2Π], y Î[-3,3 ].
ANSWER: y1 + y2 looks like this:
In[2]:=
Plot@8Sin@xD + H1  3L Sin@3 * xD<, 8x, -2 Pi, 2 Pi<,
PlotRange ® 8-3, 3<, PlotStyle ® [email protected]<, ImageSize ® 600D
3
2
1
Out[2]=
-6
-4
-2
2
-1
-2
-3
4
6
Two-Three-FourierTerms-061708-22.nb
In[1]:=
3
Plot@8Sin@xD, H1  3L Sin@3 * xD, Sin@xD + H1  3L Sin@3 * xD<, 8x, -2 Pi, 2 Pi<,
PlotRange ® 8-3, 3<, PlotStyle ® [email protected]<, ImageSize ® 600D
3
2
1
Out[1]=
-6
-4
-2
2
-1
-2
-3
4
6
4
Two-Three-FourierTerms-061708-22.nb
Ÿ The graphic below shows the curves
(y1 = Sin[x] ) + (y2 = (1/3) Sin [ 3 x ] )
y3 = (1/5) Sin [ 5 x ]
x Î[-2Π, 2Π], y Î[-3,3 ].
QUESTION: what does the curve y1 + y2 + y3 look like?
Plot@8Sin@xD + H1  3L Sin@3 * xD, H1  5L Sin@5 * xD<, 8x, -2 Pi, 2 Pi<,
PlotRange ® 8-3, 3<, PlotStyle ® [email protected]<, ImageSize ® 600D
3
2
1
-6
-4
-2
2
-1
-2
-3
Plot@8Sin@xD, H1  3L Sin@3 * xD, H1  5L Sin@5 * xD<, 8x, -2 Pi, 2 Pi<,
PlotRange ® 8-3, 3<, PlotStyle ® [email protected]<, ImageSize ® 600D
4
6
Two-Three-FourierTerms-061708-22.nb
5
EXAMPLE 2
Ÿ The graphic below shows the two curves
y1 = Cos[x] and
y2= (1/3^2) Cos [ 3 x ]
x Î[-2Π, 2Π], y Î[-3,3 ].
QUESTION: what does the curve y1 + y2 look like? See next cell for an answer.
Plot@8Cos@xD, H1  3 ^ 2L Cos@3 * xD<, 8x, -2 Pi, 2 Pi<,
PlotRange ® 8-1.5, 1.5<, PlotStyle ® [email protected]<, ImageSize ® 600D
1.5
1.0
0.5
-6
-4
-2
2
-0.5
-1.0
-1.5
Ÿ y1 = Cos[x] and
y2= (1/3^2) Cos [ 3 x ]
x Î[-2Π, 2Π], y Î[-3,3 ].
ANSWER: y1 + y2 looks like this:
4
6
6
Two-Three-FourierTerms-061708-22.nb
Plot@8Cos@xD + H1  3 ^ 2L Cos@3 * xD<, 8x, -2 Pi, 2 Pi<,
PlotRange ® 8-1.5, 1.5<, PlotStyle ® [email protected]<, ImageSize ® 600D
1.5
1.0
0.5
-6
-4
-2
2
-0.5
-1.0
-1.5
4
6
Two-Three-FourierTerms-061708-22.nb
In[3]:=
7
Plot@8Cos@xD, H1  3 ^ 2L Cos@3 * xD, Cos@xD + H1  3 ^ 2L Cos@3 * xD<, 8x, -2 Pi, 2 Pi<,
PlotRange ® 8-1.5, 1.5<, PlotStyle ® [email protected]<, ImageSize ® 600D
1.5
1.0
0.5
Out[3]=
-6
-4
-2
2
-0.5
-1.0
-1.5
4
6
8
Two-Three-FourierTerms-061708-22.nb
Ÿ The graphic below shows the curves
(y1 = Cos[x] )+ (y2= (1/3^2) Cos [ 3 x ])
and
y3 = (1/5^2) Sin [ 5 x ]
x Î[-2Π, 2Π], y Î[-3,3 ].
QUESTION: what does the curve y1 + y2 + y3 look like?
Plot@8Cos@xD + H1  3 ^ 2L Cos@3 * xD, H1  5 ^ 2L Cos@5 * xD<, 8x, -2 Pi, 2 Pi<,
PlotRange ® 8-1.5, 1.5<, PlotStyle ® [email protected]<, ImageSize ® 600D
1.5
1.0
0.5
-6
-4
-2
2
-0.5
-1.0
-1.5
Plot@8Cos@xD + H1  3 ^ 2L Cos@3 * xD + H1  5 ^ 2L Cos@5 * xD<, 8x, -2 Pi, 2 Pi<,
PlotRange ® 8-1.5, 1.5<, PlotStyle ® [email protected]<, ImageSize ® 600D
4
6