When can asinbx + ccosdx be written as Rsin(x+a)?

[thomas49th]

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 :)

 

[Dick]

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

 

[thomas49th]

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 :)

 

[rock.freak667]

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

 

[thomas49th]

cool cheers :)