Question 1112429
Here is what a {{{960^o}}} looks like,
{{{drawing(300,300,-1.1,1.3,-1.2,1.2,grid(0),
circle(0,0,1),red(arc(0,0,0.6,0.6,270,360)),
red(arc(0,0,.7,.6,180,270)),
red(arc(0,0,.7,.7,90,180)),
red(arc(0,0,.8,.7,0,90)),
red(arc(0,0,.8,.8,270,360)),
red(arc(0,0,.9,.8,180,270)),
red(arc(0,0,.9,.9,90,180)),
red(arc(0,0,1,.9,0,90)),
red(arc(0,0,1,1,270,360)),
red(arc(0,0,1.1,1,180,270)),
red(arc(0,0,1.1,1.1,120,180)),
red(triangle(-0.275,-0.476,-0.275,-0.426,-0.325,-0.476)),
locate(-0.7,-0.3,red(960^o)),
arrow(0,0,-0.6,-1.039),arrow(0,0,1.25,0),
locate(0.5,1.1,QUADRANT),locate(1.05,1.1,I),
locate(-1,1.1,QUADRANT),locate(-.45,1.1,II),
locate(0.5,-1.04,QUADRANT),locate(1.05,-1.04,IV),
locate(-1.05,-1.04,QUADRANT),locate(-.5,-1.04,III)
)}}} It's 2 turns and {{{240^o}}} (all counterclockwise, of course).
When you divide {{{960^o}}} by {{{360^o}}} the quotient is {{{2}}} and the remainder is {{{240^o}}} .
You do not need to divide (unless the angle measure is huge).
You can keep subtracting {{{360^o}}} (one turn) until you get less than one turn.
You can write that as
{{{960^o-360^o-360^o=240^o}}}  , or {{{960^o-2(360^o)=240^o}}} , or {{{960^o-720^o=240^o}}} .
Now you have to work with {{{240^o}}} , the co-terminal angle of {{{960^o}}} .
An angle measuring {{{240^o}}} is in the third quadrant,
where all the angles between {{{180^o}}} and {{{270^o}}} are located.
You can write that as 
{{{180^o<240^o<270^o}}} .
The reference angle is a symmetrical angle in quadrant I, and that angle has the same absolute value for all trigonometric functions.
For quadrant III, it is easy, you just subtract half a turn<, {{{180^o}}} ,
and that gives you the angle with the opposite ray for a terminal side:
{{{drawing(300,300,-1.1,1.3,-1.2,1.2,grid(0),
circle(0,0,1),red(arc(0,0,0.6,0.6,270,360)),
red(arc(0,0,.7,.6,180,270)),
red(arc(0,0,.7,.7,90,180)),
red(arc(0,0,.8,.7,0,90)),
red(arc(0,0,.8,.8,270,360)),
red(arc(0,0,.9,.8,180,270)),
red(arc(0,0,.9,.9,90,180)),
red(arc(0,0,1,.9,0,90)),
red(arc(0,0,1,1,270,360)),
red(arc(0,0,1.1,1,180,270)),
red(arc(0,0,1.1,1.1,120,180)),
red(triangle(-0.275,-0.476,-0.275,-0.426,-0.325,-0.476)),
locate(-0.7,-0.3,red(960^o)),
arrow(0,0,-0.6,-1.039),arrow(0,0,1.25,0),
locate(0.5,1.2,QUADRANT),locate(1.05,1.2,I),
locate(-1,1.1,QUADRANT),locate(-.45,1.1,II),
locate(0.5,-1.04,QUADRANT),locate(1.05,-1.04,IV),
locate(-1.05,-1.04,QUADRANT),locate(-.5,-1.04,III),
arrow(0,0,0.6,1.039),green(arc(0,0,1.2,1.2,-60,360)),
green(triangle(0.3,0.52,0.3,0.47,0.35,0.52)),
locate(0.4,0.6,green(240^o-180^o=60^o))
)}}} The reference angle is {{{240^o-180^o=highlight(60^o)}}} .