Question

How do you solve $\sin \theta = \dfrac{1}{2}$ ?

Answer 1

Hint : In this question we need to find the value of $\theta$ . First, we will rewrite the equation with $\theta$ at one side and remaining at the other side of the equation. Then, we will use the value from the trigonometric table to determine its ratio and the angle. Then, we will substitute the ratio and the value and finally evaluate it to determine the required answer.

Complete step-by-step answer :
Now, let us solve $\sin \theta = \dfrac{1}{2}$ .
Let $\theta = {\sin ^{ - 1}}\dfrac{1}{2}$
From the values of the trigonometric table, we know that, $\sin \left( {\dfrac{\pi }{6}} \right) = \dfrac{1}{2}$ .
Therefore we can rewrite the equation as,
$\theta = {\sin ^{ - 1}}\left( {\sin \dfrac{\pi }{6}} \right)$
By cancelling the ${\sin ^{ - 1}}$ and $\sin$ we get,
$\theta = \dfrac{\pi }{6}$
Or we can say that,
$\theta = 30^\circ$ .
So, the correct answer is “ $\theta = 30^\circ$ ”.

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.