Question

The measure of an angle in standard position is given. Find two positive angles and two negative angles that are coterminal with the given angle. (Enter your answers as a comma-separated list.)
7π/6

Answer 1

Notice the picture below

negative angles, are just angles that go "clockwise", namely, the same direction a clock hands move hmmm so....  and one revolution is just 2π

now, you can have angles bigger than 2π of course, by simply keep going around, so, if you go around 3 times on the circle, say "counter-clockwise", or from right-to-left, counter as a clock goes, 3 times or 3 revolutions will give you an angle of 6π, because 2π+2π+2π is 6π

now... say... you have this angle here... let us find another that lands on that same spot

by simply just add 2π to it :)  

$\bf \cfrac{7}{6}+2=\cfrac{19}{6}\qquad thus\qquad \cfrac{7\pi} {6}+2\pi =\cfrac{19\pi }{6} \\\\\\ \cfrac{19\pi }{6}\impliedby co-terminal\ angle$

now, that's a positive one
and  $\bf \cfrac{7}{6}-2=-\cfrac{5}{6}\qquad thus\qquad \cfrac{7\pi} {6}-2\pi =-\cfrac{5\pi }{6} \\\\\\ -\cfrac{5\pi }{6}\impliedby \textit{is also a co-terminal angle}$

to get more, just keep on subtracting or adding 2π