Can you multiply the double angle forumla?

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SUMMARY

The discussion clarifies that the expression sin(4x) cannot be directly transformed into 4sin(x)cos(x) using the double angle formula. Instead, the correct approach involves recognizing that sin(4x) can be expressed as sin(2(2x)), allowing the application of the double angle formula sin(2A) = 2sin(A)cos(A) with A set to 2x. This results in sin(4x) = 2sin(2x)cos(2x), which is the accurate representation.

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Homework Statement


I have sin4x, can I use the double angle formula and make it 4sinxcosx?


Homework Equations


double angle formula


The Attempt at a Solution


sin4x----> 4sinxcosx
 
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...try graphing both and see if they're the same.
 
musiclover55 said:

Homework Statement


I have sin4x, can I use the double angle formula and make it 4sinxcosx?
In a word, no.
The double-angle formula says that sin(2A) = 2*sin(A)cos(A).

When you use formulas, you need to be very careful to follow the pattern being used.
If you write sin(4x) as sin(2(2x)), you can use the double-angle formula, replacing A in the above by 2x.
musiclover55 said:

Homework Equations


double angle formula


The Attempt at a Solution


sin4x----> 4sinxcosx
 

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