Clarification of RSin(x+a), RCos(x+a)

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SUMMARY

The discussion clarifies the use of RSin(x+a) and RCos(x+a) transformations for expressions of the form aSin(bx) + cCos(bx). It is established that when both terms share the same frequency (b), such as in y = 3Sin(2x) + 4Cos(2x), the expression can be rewritten as RSin(bx + A) or RCos(bx + A). However, if the frequencies differ, as in y = 3Sin(2x) + 4Cos(4x), this transformation is not applicable. The participants emphasize the importance of frequency matching for successful transformation.

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Homework Statement


I want to clarify about using RSin(x+a) and RCos(x+a) for aSinbx + cCosbx

If I am given y = 3Sin2x + 4cos2x

Can I turn it into RSin(x+a) and RCos(x+a) expressions

HOWEVER

if y = 3Sin2x + 4cos4x Can I turn it into RSin(x+a) and RCos(x+a) expressions?

Thanks :)
 
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No, you can't. Try plotting that function. It doesn't look very much like a simple sin or cos graph, does it?
 
Dick said:
No, you can't. Try plotting that function. It doesn't look very much like a simple sin or cos graph, does it?

is that for

if y = 3Sin2x + 4cos4x

what about:

"I want to clarify about using RSin(x+a) and RCos(x+a) for aSinbx + cCosbx

If I am given y = 3Sin2x + 4cos2x

Can I turn it into RSin(x+a) and RCos(x+a) expressions"

or can you only do one or the other (either RSin(x+a) and RCos(x+a)) and you have to spot each one


Thanks :)
 
For asinbx+cCosbx, once those 'b's are the same, you can turn it into either Rsin(bx+A) or Rcos(bx+A).
 
cool cheers :)
 

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