I am having trouble understanding coterminal angles.
For the next set of questions, I need to find two angles coterminal with:
(a) 107pi/18
(b) 60 degrees
(c) -30 degrees
I don't just want answers. I need an explanation.
Thank you
Coterminal angles in the Cartesian plane have the same initial side and terminal side; the difference is that they can be obtained by adding or subtracting 360 degrees/2π radians, or multiples thereof. Check this site for further info:
Mathwords: Coterminal Angles
To do the problems above, just add 360 degrees/2π radians to the original angle, and subtract 360 degrees/2π radians from the original angle. For (a) this would be
and
.
What you add/subtract is arbitrary, since the directions didn't specify. I could have taken the original angle and added 720 degrees and 1080 degrees and those answers would also be valid. In other words, there are a whole lot of angles that are coterminal with each other.
01
I understood everything you said except the following:
"Coterminal angles in the Cartesian plane have the same initial side and terminal side; the difference is that they can be obtained by adding or subtracting 360 degrees/2π radians, or multiples thereof."
Can you give me an example of "multiples thereof"?
Hi magentarita,
Look at it this way. Let's say you have a 30 degree angle, initial side on the positive x-axis, terminal side in the 1st quadrant. If you add 360, you obtain a coterminal angle of 390. Multiples thereof would indicate that 30 + any multiple of 360 would also produce an angle coterminal with 30 degrees.
.
.
.
etc.