Hi;
Can someone just tell me the midpoint of
-pi/6 and 5pi/6
Thanks.
I get $\displaystyle \dfrac{11\pi}{21}$. I'm not sure how you got to twelfths from twenty-firsts (21 being the LCD of 3 and 7)
Spoiler:
More generally lets say you have a line between $\displaystyle a$ and $\displaystyle b$ and you want to find the midpoint (we'll call this $\displaystyle c$). By definition the midpoint (c) is equidistant from either end (a and b). Thus $\displaystyle b - c = c - a$.
With a little bit of manipulation: $\displaystyle b+a = 2c$ and $\displaystyle c = \dfrac{b+a}{2}$. This is the same as the (arithmetic) mean of a and b.
Seems to be a sign mistake because: $\displaystyle \frac{+\frac \pi6+\frac56 \pi}2=\frac \pi2$
How did you get this result?
$\displaystyle \frac{\frac \pi3 + \frac57 \pi}2=\frac{\frac7{21} \pi+\frac{15}{21} \pi}2$
which will never yields your result.