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The R-method:

If $R = \sqrt{a^2 + b^2}$

$a \sinθ + b \cosθ$

$= R \sin(θ + α)$, where $\tan α = \frac ba$

$=R \cos(θ − α)$, where $\tan α = \frac ab$

Its proof provided here makes some assumptions that do not seem intuitive. Is there any alternative way to prove this?

Blue
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Shub
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    What assumptions in particular are you unsure about? Expressing $a,b$ in terms of $R,\alpha$ can be most intuitively justified by drawing the point $(a,b)$ in the Cartesian plane and then figuring out what point this represents in polar coordinates. – Semiclassical Feb 10 '21 at 06:22
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    I closed as a duplicate of this question. That question's Linked list shows at least a half-dozen other incarnations. (A site search likely reveals many more, but it's tricky to search for formulas.) If none of the existing answers are satisfactory, please update your question to explain what seems to be lacking. – Blue Feb 10 '21 at 06:25
  • Thanks :) I understood – Shub Feb 10 '21 at 06:49

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