Find approximate solutions for the equation in the interval $ -\pi

Question

Find approximate solutions for the equation in the interval $ -\pi<\mathbf{X}<\pi $. Round to three decimal places.
-$\tan x = 5 \sin x$
A) $0,1.369$
B) $0,1.571$
C) $- 1.571,0,1.571$
D) $- 1.369,0,1.369$

Quizplus · Accepted Answer

The equation $\tan x = 5 \sin x$ can be rewritten as $\frac{\sin x}{\cos x} = 5 \sin x$, leading to $\sin x = 0$ or $\cos x = \frac{1}{5}$. The solutions for $\sin x = 0$ in the given interval are $x = 0$, and for $\cos x = \frac{1}{5}$, the solutions are approximately $x = \pm 1.369$, hence the correct answer is $-1.369, 0, 1.369$.

Find Approximate Solutions for the Equation in the Interval −π<X<π -\pi<\mathbf{X}<\pi −π<X<π

Find Approximate Solutions for the Equation in the Interval $-\pi<\mathbf{X}<\pi$