Does anyone know of a geometric interpretation of $a \sin\theta + b \cos\theta$? I know that it can be derived by the angle sum identity, but is there a geometric significance of this identity?
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1It's a dot product. – Qiaochu Yuan Sep 15 '23 at 09:07
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2$a \sin\theta + b \cos\theta$ is an expression, not an identity. – Martin R Sep 15 '23 at 09:10
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3Can you give some context? – Chris Lewis Sep 15 '23 at 09:56
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The identity I meant is actually this https://math.stackexchange.com/questions/948329/how-is-a-sin-theta-b-cos-theta-c-sin-theta-phi-derived. Forgot to write it down. – PunnyBunny Sep 16 '23 at 14:19
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Take a rectangle of sides $a$ and $b$ and draw two parallel lines through opposite vertices at angle $\theta$ to one of the sides.
Then your ecpression is the perpendicular distance between these two lines (for suitable choice of $\theta$).
David Quinn
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