Question

How do you evaluate \[{\sin ^{ - 1}}\left( 1 \right)\]?

Answer 1

Hint: Here, we have to evaluate the inverse of the sine function. We will use the trigonometric ratio and by rewriting the equation, we will evaluate the inverse of the sine function. A trigonometric equation is defined as an equation involving the trigonometric ratios. Trigonometric identity is an equation that is always true for all the variables.

Formula Used:
Trigonometric ratio: \[\sin 90^\circ = 1\].

Complete Step by Step Solution:
We are given a trigonometric equation \[{\sin ^{ - 1}}\left( 1 \right)\].
We know that a trigonometric ratio of \[\sin 90^\circ \] is \[1\].
\[\sin 90^\circ = 1\]
Taking sine inverse on both sides, we get
\[ \Rightarrow 90^\circ = {\sin ^{ - 1}}\left( 1 \right)\]
\[ \Rightarrow {\sin ^{ - 1}}\left( 1 \right) = 90^\circ \]
The inverse of sine \[1\] is \[90^\circ \].

Therefore, the inverse of sine \[1\] is \[90^\circ \] or \[\dfrac{\pi }{2}\].

Additional Information:
We know that we have many trigonometric identities that are related to all the other trigonometric equations. We need to remember that the trigonometric ratio and the co-trigonometric ratio is always reciprocal to each other. A trigonometric ratio is used to find the relationships between the sides of a right-angle triangle and also helps in finding the lengths of the triangle.

Note: The inverse trigonometric function is used to find the missing angles in a right-angled triangle whereas the trigonometric function is used to find the missing sides in a right-angled triangle. The range of the arcsine of the angle lies between \[ - \dfrac{\pi }{2}\] radians and \[\dfrac{\pi }{2}\] radians. The maximum of the sine of the angle is 1 and at \[\dfrac{\pi }{2}\] radians. The basic angles used in solving trigonometric problems are in degrees. The trigonometric angles can also be denoted in Radians