Checking this answer regarding a trig problem

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Homework Statement:

Prove that if A, B are given real numbers there exists C and ∝ with C ≥ 0 such that Ccos(x+∝) = Asinx + Bcosx. Determine C and ∝ if A=B=1

Relevant Equations:

cos(x+y)= cosxcosy-sinxsiny
Author gave solution [itex]C = \sqrt{2}, ∝ = -pi/4[/itex]

but plugging [itex]C = - \sqrt{2}, ∝ = -3pi/4[/itex] into cos(x+y) and leaving the x I get [itex]\sqrt{2}Cos(x+3pi/4) = sinx+cosx[/itex]

Is my answer valid as well?
 

Answers and Replies

  • #2
PeroK
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Homework Statement:: Prove that if A, B are given real numbers there exists C and ∝ with C ≥ 0 such that Ccos(x+∝) = Asinx + Bcosx. Determine C and ∝ if A=B=1
Relevant Equations:: cos(x+y)= cosxcosy-sinxsiny

Author gave solution [itex]C = \sqrt{2}, ∝ = -pi/4[/itex]

but plugging [itex]C = - \sqrt{2}, ∝ = -3pi/4[/itex] into cos(x+y) and leaving the x I get [itex]\sqrt{2}Cos(x+3pi/4) = sinx+cosx[/itex]

Is my answer valid as well?
What does your answer give at ##x = 0##?
 
  • #3
haruspex
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... with C ≥ 0 ...
...
but plugging [itex]C = - \sqrt{2}, [/itex]
 

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