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

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Homework Help Overview

The discussion revolves around the transformation of trigonometric expressions into the forms RSin(x+a) and RCos(x+a). The original poster seeks clarification on whether such transformations are applicable for different combinations of sine and cosine terms with varying coefficients and frequencies.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the conditions under which RSin(x+a) and RCos(x+a) can be used, specifically comparing cases where the sine and cosine terms have the same or different frequencies.

Discussion Status

Participants have provided differing viewpoints on the applicability of the transformations. Some suggest that the transformations are only valid when the frequencies of the sine and cosine terms are the same, while others have raised concerns about the visual representation of the functions.

Contextual Notes

The discussion includes considerations of plotting functions to assess their forms and the implications of varying coefficients and frequencies in the sine and cosine terms.

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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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