Find the range of the function $5 s i n x - 12 c o s x + 7.$

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Solution

$f (x) = 5 s i n x - 12 c o s x + 7$

$\begin{matrix} f (x) = 13 c o s α . s i n x - 13 s i n α . c o s x + 7 = 13 (c o s α . s i n x - s i n α . c o s x) + 7 = 13 (s i n (x - α)) + 7 = - 13 < 13 (s i n (x - α)) < 13 = - 6 < 13 (s i n (x - α)) + 7 < 20 \end{matrix}$

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Similar questions

5 sin x + 12 cos x

\frac{3}{5 s i n x - 12 cos x + 19}

5 sin x - 12 cos x = - 13 sin 3 x

ϕ = {sin}^{- 1} (\frac{12}{13})

5 sin x - 12 cos x = - 13 sin 3 x

sin ϕ = \frac{12}{13}

\emptyset

{s i n}^{- 1}

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