Find the value of $ arccos(-1/2) $ and verify it using the unit circle.
Answer 1
Henry Green
To find the value of $\arccos(-1/2)$, we need to determine the angle in the unit circle whose cosine is $-1/2$.
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From the unit circle, we know that:
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$ \cos(\pi – \frac{\pi}{3}) = \cos(\frac{2\pi}{3}) = -1/2 $
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Hence, the value of $\arccos(-1/2)$ is $\frac{2\pi}{3}$.
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Verification:
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Consider the angle $\frac{2\pi}{3}$ in the unit circle, its cosine value is:
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$ \cos(\frac{2\pi}{3}) = -1/2 $
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This matches our original value, verifying that $\arccos(-1/2) = \frac{2\pi}{3}$.
Answer 2
John Anderson
To find $arccos(-1/2)$, we need the angle whose cosine is $-1/2$.
We know that:
$ cos(frac{2pi}{3}) = -1/2 $
Thus, $arccos(-1/2) = frac{2pi}{3}$.
Verification: The cosine of $frac{2pi}{3}$ is:
$ cos(frac{2pi}{3}) = -1/2 $
This confirms that $arccos(-1/2) = frac{2pi}{3}$.
Answer 3
Olivia Lee
To find $arccos(-1/2)$, we determine the angle whose cosine is $-1/2$.
As:
$ cos(frac{2pi}{3}) = -1/2 $
Then, $arccos(-1/2) = frac{2pi}{3}$
Verification: Since:
$ cos(frac{2pi}{3}) = -1/2 $
This verifies that $arccos(-1/2) = frac{2pi}{3}$.
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