Question

Find approximate solution for the equation in the interval 0<_ x <_ pi. round to three decimal places. tanx=5 sin x

Answer 1

Answer:

d. 0, 1.369

Step-by-step explanation:

Given:

The equation is: $\tan x =5\sin x................(0\leq x\leq \pi)$

Adding $-5\sin x$ on both sides, we get

$\tan x - 5\sin x=0$

Using the identity $\tan x=\frac{\sin x}{\cos x}$, we get

$\frac{\sin x}{\cos x}-5\sin x=0$

Factoring out $\sin x$, we get

$\sin x(\frac{1}{\cos x}-5)=0\\\\\therefore \sin x=0\ or\ \frac{1}{\cos x}-5=0\\\\x=\sin^{-1} (0)\ or\ \cos x=\frac{1}{5}\\\\x=0\ or\ x=\cos^{-1} (\frac{1}{5})\\\\x=0\ or\ x=1.3694\approx 1.369(\textrm{Round to 3 decimal places})$

Therefore, the solution of the given equation is either 0 or 1.369.

The correct choice is d.