[Math] Finding the exact value of a trigonometric function

Question

Can someone please explain to me how i'm supposed to Find the exact value of cos (-210 degrees ).

Answer 1

I don't know if you mean degrees, but if not:

$$\cos(x) = \sum_{k=0}^{\infty} (-1)^k \frac{x^{2k}}{(2k)!} = 1-\frac{x^2}{2!}+\frac{x^4}{4!}- \cdots$$

Otherwise:

$$\cos(-210 ^\circ) = \cos(210^{\circ}) = \cos(180+30)^{\circ} \ \ \ (\text{recall}\ \cos(-x)=\cos(x))$$

$\cdot$ To finish up use angle addition for $\cos(x+y)$.