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# Help

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Let a and b be real numbers. Find the maximum value of $$a \cos \theta + b \sin \theta$$ in terms of a and b.

Aug 31, 2019

$$a \cos(\theta) + b \sin(\theta) = \\ \sqrt{a^2 + b^2}\sin(\theta + \phi),~\phi = \tan^{-1}\left(b,a\right)\\ -1 \leq \sin(\theta+\phi) \leq 1\\ \text{The max value is thus \sqrt{a^2+b^2}}$$