Express $7 \sin x - 8 \cos x$ in the form of $R \sin (x - \alpha)$, where $p, R 0$ a

Question

Express $7 \sin x - 8 \cos x$ in the form of $R \sin (x - \alpha)$, where $p, R > 0$ and $0^\circ < \alpha < 90^\circ$. Find the acute angle $x$ for which $7 \sin x - 8 \cos x = 3$. Find the minimum value of $7 \sin x - 8 \cos x$ and the corresponding value of $x$, for $0^\circ < x < 360^\circ$. the maximum value of $\frac{1}{(7 \sin x - 8 \cos x)^2 + 3}$ and the corresponding value of $x$, for $0^\circ < x < 360^\circ$.

Accepted Answer

sqrt(113) sin(x - 48.814°); (i) x = 65.2°; (ii) minimum = -sqrt(113) at x = 318.8°; (iii) maximum = 1/3 at x = 48.8° or 228.8°

Trigonometry - Trigonometric Equations

Trigonometry - Trigonometric Equations

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