Question 454990
how do you show your work for the question? 
find one angle with positive measure and one angle with negative measure coterminal with -310°
<pre>
First we draw the picture of -310°. We start at
the right side of the x-axis, then swing downward
and around in the CLOCKWISE direction through 310°,
as shown by the black CLOCKWISE arc below:

{{{drawing(400,400,-10,10,-10,10, arc(0,0,10,-10,-310,0),
red(line(-10,0,10,0),line(0,-10,0,10)),
 green(line(10cos(-310*pi/180),10sin(-310*pi/180),0,0)) 
)}}}  

Notice that 310° just lacks 50° being 360°, since 
360°-310° = 50° so the positive angle 50° measured in the 
COUNTER-CLOCKWISE direction is coterminal with -310°, as 
shown by the COUNTER-CLOCKWISE red arc below:

{{{drawing(400,400,-10,10,-10,10, arc(0,0,10,-10,-310,0),
red(line(-10,0,10,0),line(0,-10,0,10)),
 green(line(10cos(-310*pi/180),10sin(-310*pi/180),0,0)),
red(arc(0,0,8,-8,0,50)) 
)}}} 

So a positive angle coterminal with -310° is 50°.

To find a negative angle coterminal with -310, we
just need to go around 360° more in the CLOCKWISE 
direction like this:

{{{drawing(400,400,-10,10,-10,10, arc(0,0,10,-10,-180,0), arc(.5,0,11,-10,0,180), arc(0,0,12,-12, 180,360), arc(.5,0,12*1.08,(-120/11)1.08,56,180),

red(line(-10,0,10,0),line(0,-10,0,10)),
 green(line(10cos(-310*pi/180),10sin(-310*pi/180),0,0)) 
)}}}

which means we just add -360° to -310° and get -670°.

So a negative angle coterminal with -310° is -670°.

Edwin</pre>