Trigonometry

Question

Find the angle that is the least positive angle coterminal to -700°

Answer 1

go clockwise from the x-axis 360º

then go clockwise again 340º

this is -700º

the second time you went 340º clockwise you end up 20º short of the x-axis

if you go 20º counterclockwise you end up at the terminal side of angle -700º

to check if 2 angles are coterminal you subtract them and if the result is a multiple of 360º then the angles are coterminal

is 20º coterminal with -700º ?

20-(-700)=20+700=720 which is a multiple of 360

Answer 2

Okay, well -720^o would be 2 full circles, expressed in degrees. 

 

-700^o means that we have gone backwards almost 2 full circles. 

 

So, if you think about the coordinate axes, you start out to the right (positive x-axis), and then you go clockwise in a circle. When you get back to the x-axis, that was 360^o.

 

If you are almost done with 2 turns, then you are above the x-axis the same way you would be if you went counter-clockwise by 20^o.

 

So, coterminal means that you have the same (co) end point (terminal), or something like that! So, +20^o should do it!