Question 372685
find the co-terminal angle for the given angle -268 degrees


{{{drawing(400,400,-1.5,1.5,-1.5,1.5, 
line(-2,0,2,0), line(0,-2,0,2),  
green(arc(0,0,2,-2,92,360),line(0,0,3cos(92*pi/180),3sin(92*pi/180)),
locate(-1.2,.6,"-268°"),
line(cos(92*pi/180),sin(92*pi/180),cos(92*pi/180)-.1,sin(92*pi/180)-.1),
line(cos(92*pi/180),sin(92*pi/180),cos(92*pi/180)-.1,sin(92*pi/180)+.06)
)  )}}} 

Since -268° is a negative angle it is measured clockwise from the right
side of the x axis and is indicated by the green curved arrow above.

Now I will draw a positive angle which is coterminal with that -268° angle.
But it is measured clockwise with the red curved arrow below:


{{{drawing(400,400,-1.5,1.5,-1.5,1.5, 
line(-2,0,2,0), line(0,-2,0,2),  
green(arc(0,0,2,-2,92,360),line(0,0,3cos(92*pi/180),3sin(92*pi/180)),
locate(-1.2,.6,"-268°"),
line(cos(92*pi/180),sin(92*pi/180),cos(92*pi/180)-.1,sin(92*pi/180)-.1),
line(cos(92*pi/180),sin(92*pi/180),cos(92*pi/180)-.1,sin(92*pi/180)+.06)),


red(arc(0,0,2,-2,0,92),line(cos(92*pi/180)+.1,sin(92*pi/180)-.1,
cos(92*pi/180),sin(92*pi/180)),

line(cos(92*pi/180)+.1,sin(92*pi/180)+.06,
cos(92*pi/180),sin(92*pi/180)),

locate(-1.2,.6,"-268°")


)  )}}}

And that red curved arrow measured counter-clockwise from the right
side of the x-axis is found by subtracting the absolute value of the
green angle or 268° from 360° and that gives 360°-268° or 92°.

So that's the answer 92°

{{{drawing(400,400,-1.5,1.5,-1.5,1.5, 
line(-2,0,2,0), line(0,-2,0,2),  
green(arc(0,0,2,-2,92,360),line(0,0,3cos(92*pi/180),3sin(92*pi/180)),
locate(-1.2,.6,"-268°"),
line(cos(92*pi/180),sin(92*pi/180),cos(92*pi/180)-.1,sin(92*pi/180)-.1),
line(cos(92*pi/180),sin(92*pi/180),cos(92*pi/180)-.1,sin(92*pi/180)+.06)),


red(arc(0,0,2,-2,0,92),line(cos(92*pi/180)+.1,sin(92*pi/180)-.1,
cos(92*pi/180),sin(92*pi/180)),

line(cos(92*pi/180)+.1,sin(92*pi/180)+.06,
cos(92*pi/180),sin(92*pi/180)),locate(1.1,.6,"92°")

)  )}}}

Edwin</pre>