Given a point on the unit circle with coordinates $(x, y)$, if the point corresponds to an angle $ heta$ in standard position, find the angle $ heta$ if $x = -frac{1}{2}$. State your answer in radians.
Answer 1
Mia Harris
Given the point on the unit circle with coordinates $(x, y)$, we need to find $\theta$ if $x = -\frac{1}{2}$.
Since $x = -\frac{1}{2}$ on the unit circle, we can use the cosine function to find the angle. So, $\cos(\theta) = -\frac{1}{2}$.
The angles that satisfy this equation are $\theta = \frac{2\pi}{3}$ and $\theta = \frac{4\pi}{3}$ in the interval $[0, 2\pi)$.
Hence, the angles $\theta$ corresponding to $x = -\frac{1}{2}$ are:
$ \theta = \frac{2\pi}{3}, \frac{4\pi}{3} $
Answer 2
Chloe Evans
Given the point on the unit circle with coordinates $(x, y)$, if $x = -frac{1}{2}$, we can find $ heta$ by recognizing that $cos( heta) = -frac{1}{2}$.
From the unit circle, we know the angles that satisfy $cos( heta) = -frac{1}{2}$ are in the second and third quadrants.
Thus, $ heta = frac{2pi}{3}$ and $ heta = frac{4pi}{3}$ are the possible angles.
Therefore, the angles $ heta$ are:
$ frac{2pi}{3}, frac{4pi}{3} $
Answer 3
James Taylor
To find $ heta$ when $x = -frac{1}{2}$ on the unit circle, we use $cos( heta) = -frac{1}{2}$.
The angles that satisfy this are:
$ heta = frac{2pi}{3}, frac{4pi}{3} $
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