$\dfrac{11\pi}6$ and $-\dfrac{\pi}6$ have the same location on trigonometry unit circle. My question is how we can denote this property by using mathematical notation between these two fractions? For example $\frac{11\pi}6=-\frac{\pi}6$ is definitely wrong because they have different values. But does $\frac{11\pi}6\equiv-\frac{\pi}6$ makes sense?
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7$\frac{11\pi}6\equiv-\frac{\pi}6 \pmod{2\pi}$. See, for instance, "mod used to describe an angle". – Blue Jan 03 '22 at 00:25
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1Since, you mentioned unit circle and location, you could prove that they have the same x,y coords on the unit circle by somehow proving that $\cos -\frac{\pi}{6} = \cos \frac{11\pi}{6}$ and $\sin -\frac{\pi}{6} = \sin \frac{11\pi}{6}$. – Dstarred Jan 03 '22 at 00:33
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1@Blue Thanks for your help! – Amirali Jan 03 '22 at 00:54
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1$$e^{i11\pi/6}=e^{-i\pi/6}$$ – Thomas Andrews Jan 03 '22 at 01:10
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2Another word I have seen for angles like this is "coterminal" (i.e. the terminal sides of the angles coincide). – DreiCleaner Jan 03 '22 at 02:38