How do you solve $ \sin 2x = - 1 $ ?

Hint: In this question, we need to solve $ \sin 2x = - 1 $ . Here, we will take the sine to the RHS of the equation. Then, by using a trigonometric table we will write $ - 1 $ in terms of the ratio of sine. Then, by evaluating further we will determine the required answer.

Complete step-by-step answer:
Here, we need to solve $ \sin 2x = - 1 $ .
 $ \Rightarrow 2x = {\sin ^{ - 1}}\left( { - 1} \right) $
From the trigonometric table ratio we can say that
 $ \sin \left( {\dfrac{{3\pi }}{2}} \right) = - 1 $ .
Thus, substituting the value in the given equation we have,
 $ \Rightarrow 2x = {\sin ^{ - 1}}\left( {\sin \dfrac{{3\pi }}{2}} \right) $
 $ \Rightarrow 2x = \dfrac{{3\pi }}{2} $
 $ \Rightarrow x = \dfrac{{3\pi }}{4} $
Hence, the value of $ x $ is $ \dfrac{{3\pi }}{4} $ .
So, the correct answer is “ $ \dfrac{{3\pi }}{4} $ ”.

Note: Whenever we are facing these types of problems the knowledge of values of trigonometric table ratios is important. Trigonometric table involves the relationship with the length and angles of the triangle. It is generally associated with the right-angled triangle, where one of the angles is always $ 90^\circ $ .
Trigonometric ratios table helps to find the values of trigonometric standard angles $ 0^\circ ,\,30^\circ ,\,45^\circ ,\,60^\circ \,,90^\circ $ . It consists of sine, cosine, tangent, cosecant, secant, cotangent. The trigonometric table was the reason for the most digital development to take place at this rate today as the first mechanical computing devices found application through careful use of trigonometry.