Question

Find the value of \[\cos {{210}^{\circ }}\]?

Answer 1

Hint: The value of \[\cos {{210}^{\circ }}\] is simply find by using some trigonometry rules and formulas as we know \[\cos \left( 180+\theta \right)=-\cos \theta \] .
So add the \[180\] with the remaining number which is likely to be \[210-180=30\]. So, \[\theta \] must be \[30\]. So the final value will be \[-\cos {{30}^{\circ }}\].
Hence, \[\cos {{210}^{\circ }}\] is equal to \[-\cos {{30}^{\circ }}\] so as we know value of \[\cos \theta \] equals to \[\dfrac{\sqrt{3}}{2}\] according rules of trigonometry.

Complete step by step solution:
The given trigonometric equation
\[\cos {{210}^{\circ }}\]
We have, the formula for
\[\Rightarrow \cos \left( 180+\theta \right)=-\cos \theta \,\,\,...........\left( i \right)\]
So, converting the given equation in standard form.
\[\Rightarrow \cos \left( 180+{{30}^{\circ }} \right)=-\cos {{30}^{\circ }}\]
So, from \[(i)\]
\[\Rightarrow \]\[\cos \left( 180+{{30}^{\circ }} \right)=-\cos {{30}^{\circ }}\]
And
\[\Rightarrow \cos {{30}^{\circ }}=\dfrac{\sqrt{3}}{2}\]
\[=-\cos {{30}^{\circ }}\]
\[=\dfrac{\sqrt{3}}{2}\]

Note: The given equation is \[\cos \left( {{210}^{\circ }} \right).\] So always make sure that the standard rules of trigonometry equation for solving this type of equation. So learn all the trigonometry rules. Like in this question \[\cos \left( 180+\theta \right)=-\cos \theta .\]
So \[\cos \left( {{210}^{\circ }} \right)\] must be converted into \[\cos \left( 180+\theta \right)\] in order for the equation.