Expand cos^5t in Mathematica: Guide & Steps

[Dustinsfl]

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

The command expand doesn't do it.

 

[Chris L T521]

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.

 

[Ackbach]

Is
$$\cos^{5}(t)=\frac{10\cos(t)+5\cos(3t)+\cos(5t)}{16}$$
helpful?

 

[Chris L T521]

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:

TrigReduce[Cos[x]^5]

outputs what Ackbach posted above.

 

[alphy]

To expand cos^5t in Mathematica, you can use the Expand command with the PowerExpand option. Here are the steps to follow:

1. Open Mathematica and create a new notebook.
2. Type in the expression cos^5t in the first cell.
3. Right-click on the expression and select "Evaluate Cells" to see the output.
4. The output will be cos^5t.
5. To expand the expression, use the Expand command with the PowerExpand option, like this: Expand[cos^5t, PowerExpand].
6. Right-click on the expanded expression and select "Evaluate Cells" to see the output.
7. The output will be 1/8 (5 cos(5t) + 10 cos(3t) + 5 cos(t)).
8. You can also use the Simplify command to simplify the expanded expression further.
9. To save the notebook, go to File > Save As and give it a name.
10. You can now use the expanded expression in further calculations or analyses.