Question

How do you calculate ${\sin ^{ - 1}}( - 0.4)?$

Answer 1

Hint: In this question, you have to calculate the value of inverse function of sine for a particular argument. To calculate this, we need a calculator, in calculator find the value of the sine inverse of the given argument and note it also takes care of the unit either it is in radians or degrees. Since the question does not ask for a particular unit, answer with both of them (degrees and radians).

Complete step by step solution:
 In order to calculate the value of the given inverse function of sine, that is ${\sin ^{ - 1}}( - 0.4)$, we will use a scientific calculator to calculate the required value. Because we are known to some standard values only and it is impossible to remember all of the trigonometric values of a cycle with their respective arguments, that’s why we will use a scientific calculator.

To find the value of ${\sin ^{ - 1}}( - 0.4)$ on a scientific calculator follow below steps:
-Click “SHIFT” then click “SIN” (to activate the inverse function)
-Enter your value $( - 0.4)$
-Get the answer.

On calculating, we get the value of ${\sin ^{ - 1}}( - 0.4) = - {\text{23}}{\text{.5781784}}{{\text{8}}^0}$

Note: We have written the value in degrees because our calculator was set in degree mode, if you want to find value in radians then change the mode of the scientific calculator into radians. Also we have written the answer in the standard range of the inverse sine function which lies between $ - {90^0}\;{\text{to}}\;{90^0}$. So if you want the answer in general form then you can derive it by adding and subtracting it with $2n\pi ,\;n \in I$