Calculate $cos(-pi/3)$ on the unit circle
Answer 1
Chloe Evans
To find $\cos(-\pi/3)$, we first need to understand its position on the unit circle. The angle $-\pi/3$ is equivalent to rotating $\pi/3$ radians in the clockwise direction.
On the unit circle, $\pi/3$ radians is located in the first quadrant, and its coordinates are $(1/2, \sqrt{3}/2)$. Since we are rotating clockwise, we need to reflect over the x-axis, thus the coordinates become $(1/2, -\sqrt{3}/2)$.
Therefore, $\cos(-\pi/3) = \cos(\pi/3) = 1/2$.
So, $\cos(-\pi/3) = 1/2$
Answer 2
Olivia Lee
To solve for $cos(-pi/3)$ on the unit circle, recognize that $-pi/3$ is a negative angle, indicating a clockwise rotation.
The reference angle for $-pi/3$ is $pi/3$, an angle found in the first quadrant. The coordinates of $pi/3$ on the unit circle are $(1/2, sqrt{3}/2)$.
Reflecting these coordinates across the x-axis (due to the negative sign) results in $(1/2, -sqrt{3}/2)$. However, cosine represents the x-coordinate of the resulting point.
Thus, $cos(-pi/3) = cos(pi/3) = 1/2$.
Answer 3
Ava Martin
Clockwise rotation of $pi/3$ radians yields $-pi/3$. The reference angle, $pi/3$, has coordinates $(1/2, sqrt{3}/2)$ on the unit circle.
The x-coordinate remains unchanged upon reflection over the x-axis.
Therefore, $cos(-pi/3) = 1/2$.
Start Using PopAi Today