First slide

Trigonometric equations

Question

The set of all $x \in (- π, π)$ satisfying $|4 \sin x - 1| < \sqrt{5}$ is

Moderate

A

$x \in (- \frac{π}{10}, π)$
B

$x \in (- \frac{π}{10}, \frac{3 π}{10})$
C

$x \in (- π, \frac{3 π}{10})$
D

$x \in (- π, π)$

Solution

$\begin{array}{l} W e h a v e |4 \sin x - 1| < \sqrt{5} \\ \Rightarrow - \sqrt{5} < 4 \sin x - 1 < \sqrt{5} \\ \Rightarrow - (\frac{\sqrt{5} - 1}{4}) < \sin x < \frac{(\sqrt{5} + 1)}{4} \\ \Rightarrow - \sin \frac{π}{10} < \sin x < \sin \frac{3 π}{10} \\ \Rightarrow \sin (- \frac{π}{10}) < \sin x < \sin \frac{3 π}{10} \\ \Rightarrow x \in (- \frac{π}{10}, \frac{3 π}{10}) \end{array}$

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