$ ext{Calculate } cos(-pi / 3) ext{ using the unit circle}$

Using the unit circle, we know that the angle $-\pi / 3$ corresponds to moving $\pi / 3$ radians clockwise from the positive x-axis.

Since $\cos$ is the x-coordinate of the point on the unit circle, and moving $\pi / 3$ radians clockwise is the same as moving $2\pi – \pi / 3 = 5\pi / 3$ radians counterclockwise from the positive x-axis, we need to find the cosine of $5\pi / 3$.

On the unit circle, the coordinates of the angle $5\pi / 3$ are $(\frac{1}{2}, -\frac{\sqrt{3}}{2})$. Therefore, the value of $\cos(5\pi / 3)$, corresponding to $\cos(-\pi / 3)$, is $\frac{1}{2}$.

$\cos(-\pi / 3) = \frac{1}{2}$

First, let’s convert the angle $-pi / 3$ to a positive equivalent by adding $2pi$.

So, $-pi / 3 + 2pi = 2pi – pi / 3 = 6pi / 3 – pi / 3 = 5pi / 3$.

Next, we locate $5pi / 3$ on the unit circle. The coordinates for this angle are $(frac{1}{2}, -frac{sqrt{3}}{2})$.

Thus, the cosine of $5pi / 3$ is $frac{1}{2}$. Therefore, $cos(-pi / 3) = frac{1}{2}$.

$cos(-pi / 3) = frac{1}{2}$

We can find $cos(-pi / 3)$ by knowing that $cos$ is an even function, which means $cos(-x) = cos(x)$.

So, $cos(-pi / 3) = cos(pi / 3)$.

From the unit circle, $cos(pi / 3) = frac{1}{2}$.

Thus, $cos(-pi / 3) = frac{1}{2}$.

$cos(-pi / 3) = frac{1}{2}$

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