For my math homework, I have to find an angle of rotation, $\theta$, by cos $\theta$ = $-\sqrt3/2$. When I plug this into my calculator, I get 5$\pi$/6, but the correct answer is -5$\pi$/6. What is the procedure to find the correct angle.
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They are both correct as $\cos\left(\frac {5\pi}6\right)=\cos\left(-\frac {5\pi}6\right)$. You can arrive at this conclusion either geometrically or using the fact that $\cos$ is an even function. – Git Gud Nov 25 '13 at 00:04
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You have to use the context to figure out which angle is called for. For both sine and cosine, there will be two angles with the given value.
Eric Auld
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But −√3/2 is in the 2nd quadrant, and so is 5pi/6. I'm not following the geometry. – Shankar Kumar Nov 25 '13 at 00:17
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$-\sqrt{3}/2$ is not in any quadrant, since it doesn't represent an angle. $5\pi/6$ is in the second quadrant, and $-5\pi/6$ is in the third quadrant. – Eric Auld Nov 25 '13 at 00:53