In Maple or Mathematica, how can I reduce cos(a*n*pi) or sin(a*n*pi)?
To reduce cos(a*n*pi) or sin(a*n*pi) in
Maple or Mathematica, follow the appropriate instructions below.
Note: The n in the question is an
integer, and a is an unknown parameter; this is useful
for spectral analysis (i.e., Fourier series). Also, the information
below may require a nonproportional font to make sense.
Maple
In Maple, the command is:
> expand(cos(6*a*x));The above command returns:
32 cos(a x)^6 - 48 cos(a x)^4 + 18 cos(a x)^2 - 1Mathematica
In Mathematica, the command is:
In[1]:= TrigExpand[Cos[6 a x]]This command returns a polynomial in cos(a x) and sin(a x):
Out[1]= Cos[a x]^6 - 15 Cos[a x]^4 Sin[a x]^2 + 15 [a x]^2Sin[a x]^4 - Sin[a x]^6For more about statistical and mathematical software, email the UITS Stat/Math Center, visit the center's web page, or phone 812-855-4724 (IUB) or 317-278-4740 (IUPUI). The center is located in Bloomington at 410 N. Park Avenue, and is open for consultation by appointment Monday-Friday 9am-5pm.
Last modified on January 28, 2011.
