Expand cos^5t in Mathematica: Guide & Steps

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SUMMARY

The discussion focuses on expanding the expression cos^5(t) in Mathematica. Users discovered that the standard 'expand' command is ineffective for this purpose. Instead, the command TrigReduce[Cos[x]^5] successfully transforms cos^5(t) into first-degree terms of sine and cosine, yielding the result cos^5(t) = (10cos(t) + 5cos(3t) + cos(5t))/16. This method provides a clear solution for users needing to express cos^5(t) in a simplified form.

PREREQUISITES
  • Familiarity with Mathematica commands and syntax
  • Understanding of trigonometric identities and transformations
  • Basic knowledge of sine and cosine functions
  • Experience with mathematical expressions and simplification techniques
NEXT STEPS
  • Explore additional Mathematica commands for trigonometric simplifications
  • Learn about the use of TrigExpand for expanding trigonometric expressions
  • Investigate the implications of TrigReduce in complex trigonometric equations
  • Study the derivation and applications of trigonometric identities in mathematical analysis
USEFUL FOR

Mathematics students, educators, and anyone utilizing Mathematica for trigonometric calculations will benefit from this discussion.

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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