Question

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

Answer 1

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.