# Thread: Coterminal Angles Work How Again?

1. ## Coterminal Angles Work How Again?

Ok, so let me start by saying that this is my first post here, so I am sory if I do anything wrong, or If this is not the right place to post. If so, it is entirely un-intentional and I will do whatever I can to fix this mistake.

I am 16, homeschooled, and teach myself. Most of you are probably wondering why I am not just asking my parents how coterminal angles work. Im not asking my parents, because I made a deal with them when I was 5 that I could homeschool as long as I didnt need their help.

So, now that you understand why I'm here, lets get to the question.

My understanding of coterminal angles is this:
A coterminal angles share the same terminal line.

By this defenition, each angle has infinite coterminal angles.

So if this is true, why do the practice problems only have one answer?

Laim.

2. Originally Posted by Wierd
Ok, so let me start by saying that this is my first post here, so I am sory if I do anything wrong, or If this is not the right place to post. If so, it is entirely un-intentional and I will do whatever I can to fix this mistake.

I am 16, homeschooled, and teach myself. Most of you are probably wondering why I am not just asking my parents how coterminal angles work. Im not asking my parents, because I made a deal with them when I was 5 that I could homeschool as long as I didnt need their help.

So, now that you understand why I'm here, lets get to the question.

My understanding of coterminal angles is this:
A coterminal angles share the same terminal line.

By this defenition, each angle has infinite coterminal angles.

So if this is true, why do the practice problems only have one answer?

Laim.

Hi Wierd,

You are right about the definition of coterminal angles. They all have the same terminal side.

The practice problems probably (and I'm guessing here) are asking what coterminal angle between 0 and 360 degrees is equivalent to the given angle.

For example: What coterminal angle between 0 and 360 degrees is equivalent to 450 degrees.

Answer: 450 - 360 = 90 degrees

Another answer would be -270 degrees if the range were to be changed to -360 < angle < 360.

Does that help at all? The answer depends upon the range which should be given in the exercise.

3. To rephrase/supplement masters, with the hope of furthering your understanding...

"each angle has [an infinite number] of coterminal angles" would be a more accurate statement, and you are right in questioning how they can come up with just one answer!

It would be like us defining "co-decimal" to mean numbers that have the same stuff after the decimal. So 4.391 and 1985.391 and -2.391 would all be co-decimal because they all have "391" after the decimal.
If I asked for a number that is co-decimal to 4.391 but is between, say, 8 and 9, you could easily answer 8.391

In our co-decimal example, it's easy to go between co-decimal numbers; you just add or subtract 1 (or any integer) until you're in the desired range.

Now for coterminal angles, the process is identical; we are just adding/subtracting 360degrees (or 2π radians...) until we land in the desired range.

4. Thank you so much for the fast reply guys! I totaly get it now!

5. You are welcome! Come back anytime.