Question

\cos \left(\frac{5\pi }{3}\right)

Answer 1

To find \(\cos\left(\frac{5\pi}{3}\right)\), we first simplify the angle:

\[
\frac{5\pi}{3} = 2\pi - \frac{\pi}{3}
\]

This means that \(\frac{5\pi}{3}\) is in the fourth quadrant (since \(2\pi\) corresponds to a full rotation and we subtract \(\frac{\pi}{3}\)).

In the fourth quadrant, the cosine function is positive. Therefore,

\[
\cos\left(\frac{5\pi}{3}\right) = \cos\left(-\frac{\pi}{3}\right) = \cos\left(\frac{\pi}{3}\right)
\]

Now we know that:

\[
\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}
\]

Thus,

\[
\cos\left(\frac{5\pi}{3}\right) = \frac{1}{2}
\]

So the final answer is:

\[
\cos\left(\frac{5\pi}{3}\right) = \frac{1}{2}
\]