Expand cos^5t in Mathematica: Guide & Steps

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Discussion Overview

The discussion revolves around how to expand the expression cos^5(t) in Mathematica, exploring different commands and methods for achieving this expansion, particularly in terms of sine and cosine functions. The focus includes both theoretical understanding and practical application within Mathematica.

Discussion Character

  • Technical explanation, Conceptual clarification, Experimental/applied

Main Points Raised

  • One participant inquires about the command needed to expand cos^5(t), noting that the command 'expand' does not work for this purpose.
  • Another participant suggests that if the goal is to express cos^5(t) in first degree terms of sine and cosine, 'expand' may not be the appropriate command, and they are unsure of an alternative.
  • A mathematical expression is presented, stating that $$\cos^{5}(t)=\frac{10\cos(t)+5\cos(3t)+\cos(5t)}{16}$$, which is proposed as a potential solution.
  • A later reply confirms that the expression provided is indeed the output of the command TrigReduce[Cos[x]^5] in Mathematica, indicating that this command can be used to achieve the desired expansion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best command to use for expanding cos^5(t), but there is agreement on the usefulness of the TrigReduce command as a method to obtain the expression in a different form.

Contextual Notes

Some limitations are noted regarding the clarity of the commands available in Mathematica for this specific expansion, as well as the potential for misunderstanding the intended form of the expansion (first degree terms vs. other forms).

Dustinsfl
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How can I tell Mathematica to expand cos^5 t?

The command expand doesn't do it.
 
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dwsmith said:
How can I tell Mathematica to expand cos^5 t?

The command expand doesn't do it.

Are you trying to write it in first degree terms of sine and cosine? If so, expand isn't the command to do this and I don't know off the top of my head if there is one that would do such a thing.
 
Is
$$\cos^{5}(t)=\frac{10\cos(t)+5\cos(3t)+\cos(5t)}{16}$$
helpful?
 
Ackbach said:
Is
$$\cos^{5}(t)=\frac{10\cos(t)+5\cos(3t)+\cos(5t)}{16}$$
helpful?

I learned something new today; I didn't realize that this was an option in Mathematica. The command:

Code: 
TrigReduce[Cos[x]^5]

outputs what Ackbach posted above.
 

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