Question

How do you use a calculator to find $\sin \left( x \right)=\dfrac{3}{5}$ ?

Answer 1

Here we have to calculate the value of the given trigonometric function using a calculator. Firstly as we have to find the value of $x$ we will take the sine term on the right hand side and it will become the sine inverse. Then using a calculator we will find the value of ${{\sin }^{-1}}\dfrac{3}{5}$ and get our desired answer.

Complete step by step answer:
We have use calculator for finding the value of below equation:
$\sin \left( x \right)=\dfrac{3}{5}$
Now as we want $x$ value so we will take the sine term on the right hand side as follows:
$x={{\sin }^{-1}}\left( \dfrac{3}{5} \right)$….$\left( 1 \right)$
Now as we have to use a calculator, use a scientific one as it has more function and trigonometric function values can be obtained by it.
First step is to use your calculator by using the “ON” key on the top right corner. Now press “shift” key then “sin” key the outcome will come as ${{\sin }^{-1}}$ on your screen.
Now press the open bracket button and type $3\div 5$ and close the bracket.
The value will appear as ${{\sin }^{-1}}\left( 3\div 5 \right)$ on your screen then press enter.
The answer will come as $36.869$ substituting the value in equation (1) we get,
$\Rightarrow x=36.869$
Approximately we can write it as,
$x=36.9$
Hence solution of $\sin \left( x \right)=\dfrac{3}{5}$ is $x=36.9$

Note:
Calculator is very useful for finding the value of a trigonometric function or other higher function. As we can see that we have taken the sine function on the right and it became an inverse function this step is very important as if we calculate $\sin \left( \dfrac{3}{5} \right)$ value it will come out different. The bracket is very important while using a calculator as if we don’t put it and try to find the value of ${{\sin }^{-1}}3\div 5$ the calculator will show “Math ERROR”.