Find the maximum value of $3\sin x + 4\cos x$.
A$7$
B$12$
C$5$CORRECT
D$\sqrt{7}$
JUPEBMathematicsTrigonometry
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Why the answer is C, and why the others tempt you.
Write $3\sin x + 4\cos x = R\sin(x + \alpha)$ where $R = \sqrt{3^2 + 4^2} = 5$. Since $\sin(x + \alpha)$ has a maximum of 1, the maximum value of the expression is 5. Simply adding the coefficients gives 7, which the expression never reaches.
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