Find the value of $cos(-pi/3)$ on the unit circle

To find the value of $\cos(-\pi/3)$ on the unit circle, we should first recall the basic properties of the cosine function and the unit circle:

1. The cosine function is an even function, meaning $\cos(-x) = \cos(x)$.

2. Therefore, $\cos(-\pi/3) = \cos(\pi/3)$.

3. We know from the unit circle that $\cos(\pi/3) = \frac{1}{2}$.

Hence, the value of $\cos(-\pi/3)$ is:

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

To determine the value of $cos(-pi/3)$, let’s use the properties of trigonometric functions and the unit circle:

1. Remember the property of the cosine function: $cos(-x) = cos(x)$. This holds because cosine is an even function.

2. Applying this property, $cos(-pi/3) = cos(pi/3)$.

3. From the unit circle, the cosine of $pi/3$ corresponds to the x-coordinate of the point where the angle intercepts the unit circle.

4. For $pi/3$, this point is $left(frac{1}{2}, frac{sqrt{3}}{2}
ight)$. Thus, $cos(pi/3) = frac{1}{2}$.

Therefore, the value of $cos(-pi/3)$ is:

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

To find $cos(-pi/3)$ on the unit circle, recall that cosine is an even function:

1. $cos(-x) = cos(x)$

2. Hence, $cos(-pi/3) = cos(pi/3)$

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

So,

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

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