Question

How do you find the exact value of \[\sin \left( \dfrac{\pi }{6} \right)\] ?

Answer 1

Hint: In the radian system and the degree system we know a common relation and that is \[\pi =180{}^\circ \].
If we have to find the value of trigonometric functions if it is given in radian or in terms of \[\pi \] then assume \[\pi \] be \[180{}^\circ \] . As in this question we will put \[180{}^\circ \] in place of \[\pi \] then we will get a numerical value in the \[\sin \] angle and we know the value of trigonometric functions.

Complete step by step solution:
\[\sin \left( \dfrac{\pi }{6} \right)=?\]
Since we know that \[\pi =180{}^\circ \] is a relation between degree and radian system then put \[180{}^\circ \] in place of \[\pi \]
\[\Rightarrow \sin \left( \dfrac{\pi }{6} \right)=\sin \left( \dfrac{180{}^\circ }{6} \right)\]
\[\Rightarrow \sin 30{}^\circ \]
Now the value of \[\sin 30{}^\circ \] is known to us and that is \[\dfrac{1}{2}\]

Hence, \[\sin \left( \dfrac{\pi }{6} \right)=0.5\].

Note:
When the radian system is introduced in the question, first convert I into the degree as we are familiar with the degree system and it is quite easy to simplify without any confusion and then just put the value of the trigonometric functions that are already known to us.