Question

How do you evaluate arcsin on a calculator?

Answer 1

Hint: In the given question, you have been asked about to find the arcsin function on a calculator. To evaluate, you should know about the basic trigonometric function. The inverse trigonometric functions are usually the 2nd functions of the trigonometric function. The inverse function of sine is, \[{{\sin }^{-1}}x\], is also called the arcsine, \[\arcsin \left( x \right)\]. The arcsine function is the inverse of the sine function as long as the sin function is restricted to a certain domain.

Complete step by step solution:
Arcsin represents this equation:
Let,
\[y=\sin \theta \]
\[\Rightarrow\dfrac{1}{\sin }y=\theta \]
\[\Rightarrow{{\sin }^{-1}}y=\theta \]
Therefore, if y is the sine of θ, then θ is the arcsin of y. The arcsin is the inverse of the sine function.

Following are the steps followed to evaluate arcsin on a calculator:
-To calculate arcsin on the calculator, press the "2nd" button and then the "\[\sin \]" button. -This will produce the "\[{{\sin }^{-1}}\]" button.
-Enter the value in the calculator you want to calculate.
-After entering the value, press enter.
-The answer will appear on the screen, and in this way you evaluate arcsin on a calculator.

For example, you wish to calculate the arcsin of 2. First, press "2nd". Next, press "sin," and "\[{{\sin }^{-1}}\]" will appear. Then press 2, and the equation will appear as \[{{\sin }^{-1}}\left( 2 \right)\]. Press "Enter" to calculate the answer. You will get your answer.

By convention, the range of arcsin is lies between \[\left[ -\dfrac{\pi }{2},\dfrac{\pi }{2} \right]\], so if we use calculator to solve any arcsin, out of the infinite possibilities, it would give us that answer which is the one in the range of the function.

Additional information:
Most calculators don’t have \[\left( \sec \right),\ \left( \cos ec \right)\ and\ \left( \cot \right)\] functions so that you have to type in:
-\[\left( \dfrac{1}{\sin x} \right)\] in the place of \[\sec \left( x \right)\]
-\[\left( \dfrac{1}{\cos x} \right)\]in the place of \[\cos ec\left( x \right)\]
-\[\left( \dfrac{1}{\tan x} \right)\] in the place of \[\cot \left( x \right)\].

Note: When you are finding the arcsin or any other trigonometric function, you should have memorized the location of the keys such as arcsin, cos function, etc. beforehand. By doing this you will be more efficient on time-limit tests. The inverse trigonometric functions are generally the second functions of the trigonometric buttons.