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 $$\cos (180+\theta )=-\cos \theta$$ .
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 $${\displaystyle \frac{\sqrt{3}}{2}}$$ according rules of trigonometry.

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

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 $$\cos (180+\theta )=-\cos \theta .$$
So $$\cos \left({210}^{\circ }\right)$$ must be converted into $$\cos (180+\theta )$$ in order for the equation.