Find the coordinates on the unit circle for the angle corresponding to $-frac{2}{3}pi$ radians
Answer 1
Chloe Evans
To find the coordinates on the unit circle for the angle corresponding to $-\frac{2}{3}\pi$ radians, we first determine the reference angle. The reference angle is $\frac{2}{3}\pi$ radians.
The coordinates for $\frac{2}{3}\pi$ radians are $(\cos(\frac{2}{3}\pi), \sin(\frac{2}{3}\pi))$.
Calculating these values, we get:
$\cos(\frac{2}{3}\pi) = -\frac{1}{2}$
$\sin(\frac{2}{3}\pi) = \frac{\sqrt{3}}{2}$
Since the angle is negative, the coordinates will be in the third quadrant, so both values will be negative:
$\cos(-\frac{2}{3}\pi) = -\frac{1}{2}$
$\sin(-\frac{2}{3}\pi) = -\frac{\sqrt{3}}{2}$
Therefore, the coordinates are: $(-\frac{1}{2}, -\frac{\sqrt{3}}{2})$
Answer 2
Ella Lewis
To determine the coordinates on the unit circle for an angle of $-frac{2}{3}pi$ radians, we convert the angle into its positive equivalent:
$2pi – frac{2}{3}pi = frac{6}{3}pi – frac{2}{3}pi = frac{4}{3}pi$
The coordinates at $frac{4}{3}pi$ are:
$cos(frac{4}{3}pi) = -frac{1}{2}$
$sin(frac{4}{3}pi) = -frac{sqrt{3}}{2}$
Therefore, the coordinates for the angle $-frac{2}{3}pi$ on the unit circle are:
$(cos(-frac{2}{3}pi), sin(-frac{2}{3}pi)) = (-frac{1}{2}, -frac{sqrt{3}}{2})$
Answer 3
Christopher Garcia
The coordinates for the angle $-frac{2}{3}pi$ on the unit circle are:
$ cos(-frac{2}{3}pi) = -frac{1}{2} $
$ sin(-frac{2}{3}pi) = -frac{sqrt{3}}{2} $
Thus, the coordinates are $(-frac{1}{2}, -frac{sqrt{3}}{2})$.
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