Find the value of $cos(-pi/3)$ on the unit circle
Answer 1
Henry Green
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:
$\cos(-\pi/3) = \frac{1}{2}$
Answer 2
John Anderson
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:
$cos(-pi/3) = frac{1}{2}$
Answer 3
Samuel Scott
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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