Question

Find the measures of two angles, one positive and one negative, that are coterminal with pi/5.

Answer 1

So what are coterminal angles? Two angles are coterminal if they have the same terminal side.

In geometry or picture view, it is easy to see a coterminal angle. But from mathematical point of view, we can see it as following:

A is an angle
Then coterminal of A should be: \[A \pm k.2\pi\] with k is an integter number (k can be any negative like -1 or positive numbers +1, +2, ....)

In your question, \[A = \pi/5 \rightarrow B = A \pm k.2\pi = \pi/5 \pm k.2\pi\]

For example, if you want a positive angle, then you may try k = +1, \[B = 11\pi/5\]

A negative angle, you may try k = -1, \[B = -9\pi/5\]

Answer 2

I have answer choices:
\[ 11\pi/5;-9\pi/5,
\pi/5 + 360degrees; \pi/5 - 360degrees,
6\pi/5;-4\pi/5, 11\pi/5;-\pi/5\]

Answer 3

One of my choices was 11pi/5, and -9/5. Is that right?

Answer 4

http://hotmath.com/hotmath_help/topics/coterminal-angles.html

Answer 5

yes, you right, :) there are many options, but the easiest one is to assign k = +/- 1

Answer 6

pi/5 + 2pi = pi/5 + 10pi/5 = 11pi/5
and
pi/5 - 2pi

Answer 7

Thank you @DSS , but I'm confused on how pi/5 + 2pi = 11pi/5. Can you explain that?

Answer 8

\[\frac{ 1 }{ 5 } + 2 = \frac{ 1 + 10 }{ 5 }\]

Answer 9

Is that because you faound a common denominator, so you really did 1/5 + 10/5? Because it started as 2/1, and you multiplied by 5?

Answer 10

Yes, actually, this is very basic pre-algebra

Answer 11

Okay, then I understand it now. That website she linked made it simple. I don't know why my class website can't just explain it that way. They try to make it so confusing..

Answer 12

Thank you guys again. I only have two more questions! haha. Then maybe I will be able to do all of this on my own. :)