Find the angle whose cosine is $-frac{2}{3}$ using the unit circle.
Answer 1
Henry Green
To find the angle whose cosine is $-\frac{2}{3}$, we need to look at the unit circle and identify the angles where the x-coordinate (cosine value) is $-\frac{2}{3}$. Since cosine is negative in the second and third quadrants, we look in those regions.
Thus, we have:
$\theta = \cos^{-1}(-\frac{2}{3})$
and
$\theta = 2\pi – \cos^{-1}(-\frac{2}{3})$
These angles in degrees are approximately:
$\theta \approx 131.81^\circ$
and
$\theta \approx 228.19^\circ$
Answer 2
Emma Johnson
To find the angle whose cosine is $-frac{2}{3}$ on the unit circle, we use the inverse cosine function.
The cosine function is negative in the second and third quadrants. Therefore, the angle is:
$ heta = cos^{-1}(-frac{2}{3})$
For the second quadrant angle, we have:
$ heta approx 131.81^circ$
For the third quadrant angle:
$ heta approx 180^circ + (180^circ – 131.81^circ) = 228.19^circ$
Answer 3
Matthew Carter
We need to find the angle whose cosine is $-frac{2}{3}$.
Cosine is negative in the second and third quadrants, so:
$ heta = cos^{-1}(-frac{2}{3}) = 131.81^circ$
and
$ heta = 360^circ – 131.81^circ = 228.19^circ$
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