Question

How do you solve $\sin \theta = - 0.5$?

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 it $\sin \theta = - 0.5$.
Convert the decimal in fraction by multiplying and dividing by 10,
$ \Rightarrow \sin \theta = - \dfrac{5}{{10}}$
Cancel out common factors from numerator and denominator,
$ \Rightarrow \sin \theta = - \dfrac{1}{2}$ ….. (1)
From the values of the trigonometric table, we know that,
$ \Rightarrow \sin \left( { - \dfrac{\pi }{6}} \right) = - \dfrac{1}{2}$ ….. (2)
Equating equation (1) and (2), we get
$ \Rightarrow \sin \theta = \sin \left( { - \dfrac{\pi }{6}} \right)$
Cancel out sin from both sides,
$ \Rightarrow \theta = - \dfrac{\pi }{6}$

Hence, the value of $\theta $ is $ - \dfrac{\pi }{6}$.

Note:
Whenever we are facing these types of problems the knowledge of values of trigonometric table ratios is important. The trigonometric table involves the relationship between the length and angles of the triangle. It is generally associated with the right-angled triangle, where one of the angles is $90^\circ $.
The 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.
Trigonometry is one of the significant branches throughout the entire existence of mathematics and this idea is given by a Greek mathematician Hipparchus.