Question 1154795
<pre>
The angle -800° is measured clockwise since it's negative.
We divide its absolute value 800 by 360 to get its quotient
and remainder.  

   <u>   2</u>
360)800
    <u>720</u>
     80

The quotient of 2 tells us that the angle goes around 2 times.
The negative sign tells us that the rotation is clockwise.
The remainder of 80 tells us that after going around 2 times,
it goes 80° further in the clockwise direction.  So we draw
the angle and the terminal side.

{{{drawing(200,200,-10,10,-10,10,
line(-12,0,12,0), line(0,-12,0,12),
line(0,0,.87,-4.92),
arc(-.5,0,3,-3,180,360),
arc(0,0,4,-4,0,180),
arc(-.5,0,5,-5,180,360),
arc(0,0,6,-6,0,180),
arc(-.5,0,7,-7,290,360))}}}

We see that it ends up in the 4th quadrant and since the remainder
80° is less than 90°, it means the reference angle is 80°.

The angle between 0° and 360° that is in the 4th quadrant is gotten
by subtracting 80° from 360° getting 280°.

So -800° is coterminal with 280°

{{{drawing(200,200,-10,10,-10,10,
line(-12,0,12,0), line(0,-12,0,12),
line(0,0,.87,-4.92),
arc(0,0,6,-6,0,280))}}}

Edwin</pre>