# Thread: Coterminal Angles

1. ## Coterminal Angles

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

2. Originally Posted by magentarita
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
$\frac{107\pi}{18} + 2\pi = \frac{107\pi}{18} + \frac{36\pi}{18} = \frac{143\pi}{18}$ and
$\frac{107\pi}{18} - 2\pi = \frac{107\pi}{18} - \frac{36\pi}{18} = \frac{71\pi}{18}$ .

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

3. ## good but...

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"?

4. Originally Posted by magentarita
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"?
do you know that

$\pi=180^o$

so when add [tex]2\pi[tex] it is the same as when you add $360^o$

multiples thereof :

example
$\frac{\pi}{3}=\frac{\pi}{3}+2\pi=\frac{\pi}{3}+4\p i.....$

in degrees

$75^o=75^o+360^o=75^o+2(360^o)=75^o-360^o.....$

so for any angle in rad or in degree

$\theta=\theta\pm2n\pi......\forall n\in R$

angle in degree let me call it phi

$\phi=\phi\pm n(360^o)....\forall n\in R$

5. Originally Posted by magentarita
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.

$30 + {\color {red}1}(\pm360) = 390 \ \ or \ \ -330$

$30 + {\color{red}2}(\pm360) = 750 \ \ or \ \ -690$
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