find the function value using coordinates of points on the unit circle. give an exact answer. cos(-π/6)…

find the function value using coordinates of points on the unit circle. give an exact answer. cos(-π/6) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. cos(-π/6)=□ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression) b. cos(-π/6) is undefined.

find the function value using coordinates of points on the unit circle. give an exact answer. cos(-π/6) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. cos(-π/6)=□ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression) b. cos(-π/6) is undefined.

Answer

Explanation:

Step1: Recall cosine property

Cosine is an even - function, i.e., $\cos(-\theta)=\cos(\theta)$. So, $\cos\left(-\frac{\pi}{6}\right)=\cos\left(\frac{\pi}{6}\right)$.

Step2: Use unit - circle coordinates

On the unit circle, for the angle $\theta = \frac{\pi}{6}$, the coordinates of the corresponding point are $\left(\cos\frac{\pi}{6},\sin\frac{\pi}{6}\right)=\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$. So, $\cos\left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}$.

Answer:

A. $\cos\left(-\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}$