Question

How do you solve $3\sin x+2=0$?

Answer 1

Hint: To solve the given equation first we will subtract 2 from both sides of the equation. Then we will divide the obtained equation by 3. We get the value of $\sin x$. Then by calculating the inverse we get the desired answer.

Complete step by step solution:
We have been given that $3\sin x+2=0$.
We have to solve the given equation.
Now, to solve the given equation first we will subtract 2 from both sides of the equation. Then we will get
$\Rightarrow 3\sin x+2-2=0-2$
Now, simplifying the above obtained equation we will get
$\Rightarrow 3\sin x=-2$
Now, dividing the above obtained equation by 3 we will get
$\Rightarrow \dfrac{3\sin x}{3}=-\dfrac{2}{3}$
Now, simplifying the above obtained equation we will get
$\Rightarrow \sin x=-\dfrac{2}{3}$
Now, taking an inverse function we will get
$\Rightarrow x={{\sin }^{-1}}\left( -\dfrac{2}{3} \right)$
By using the calculator we get the value as
$\Rightarrow x={-0.729}^{c}$
Hence above is the required answer.

Note: If we get the general value of $\sin x$ which is given in the trigonometric ratio table, it is easy to calculate the value. We can also solve the question in alternative way as:
We get the value by simplifying the equation as
$\Rightarrow \sin x=-\dfrac{2}{3}$
Now, we know that there is no direct value given in the trigonometric ratio table. So when we approximate value we will get
$\Rightarrow x=-41.81{}^\circ $
Or we can write this as
 $\begin{align}
  & \Rightarrow x=-180+41.81{}^\circ \\
 & \Rightarrow x=-138.19 \\
\end{align}$
Hence we get the value of x.