To find the exact value of [tex]\(\cos \left( \frac{-\pi}{6} \right)\)[/tex], let's proceed through the following steps:
1. Understanding the function property:
[tex]\(\cos\)[/tex] is an even function, which means [tex]\(\cos(-x) = \cos(x)\)[/tex]. Therefore:
[tex]\[
\cos \left( \frac{-\pi}{6} \right) = \cos \left( \frac{\pi}{6} \right)
\][/tex]
2. Knowing the value of cosine for [tex]\(\frac{\pi}{6}\)[/tex]:
Remember from trigonometric values that:
[tex]\[
\cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2}
\][/tex]
3. Combining the results:
Hence, [tex]\(\cos \left( \frac{-\pi}{6} \right)\)[/tex] is exactly the same as [tex]\(\cos \left( \frac{\pi}{6} \right)\)[/tex]:
[tex]\[
\cos \left( \frac{-\pi}{6} \right) = \frac{\sqrt{3}}{2}
\][/tex]
Therefore, the exact value of [tex]\(\cos \left( \frac{-\pi}{6} \right)\)[/tex] is [tex]\( \frac{\sqrt{3}}{2} \)[/tex].
