Problem 369

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Problem 369: (2017 AMC12A, 15)

Let $f(x) = \sin{x} + 2\cos{x} + 3\tan{x}$, using radian measure for the variable $x$. In what interval does the smallest positive value of $x$ for which $f(x) = 0$ lie? $\textbf{(A)}\ (0,1) \qquad$ $ \textbf{(B)}\ (1, 2) \qquad$ $\textbf{(C)}\ (2, 3) \qquad$ $\textbf{(D)}\ (3, 4) \qquad$ $\textbf{(E)}\ (4,5)$

Solution

Exercise 369: Solution

Let $f(x)=\sin x+3\cos x+2\tan x$. In what unit interval does the smallest positive $x$ with $f(x)=0$ lie?

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