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
$\displaystyle \frac{107\pi}{18} + 2\pi = \frac{107\pi}{18} + \frac{36\pi}{18} = \frac{143\pi}{18}$ and
$\displaystyle \frac{107\pi}{18} - 2\pi = \frac{107\pi}{18} - \frac{36\pi}{18} = \frac{71\pi}{18}$ .
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
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
$\displaystyle \pi=180^o$
so when add [tex]2\pi[tex] it is the same as when you add $\displaystyle 360^o$
multiples thereof :
example
$\displaystyle \frac{\pi}{3}=\frac{\pi}{3}+2\pi=\frac{\pi}{3}+4\p i.....$
in degrees
$\displaystyle 75^o=75^o+360^o=75^o+2(360^o)=75^o-360^o.....$
so for any angle in rad or in degree
$\displaystyle \theta=\theta\pm2n\pi......\forall n\in R$
angle in degree let me call it phi
$\displaystyle \phi=\phi\pm n(360^o)....\forall n\in R$
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.
$\displaystyle 30 + {\color {red}1}(\pm360) = 390 \ \ or \ \ -330$
$\displaystyle 30 + {\color{red}2}(\pm360) = 750 \ \ or \ \ -690$
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etc.