hi can anyone help me with coterminal angles, specifically finding coterminal angles between 0 and 2

[mystic furnace]

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[shell falcon]

How are we supposed to know if we're willing without the pictures?

[haughty burrow]

Mb here is the picture

[shell falcon]

Okay, so suppose I have some angle, theta. What is the set of all angles coterminal to theta?

[haughty burrow]

What do you mean by this

[shell falcon]

...I'm not sure how that could possibly be confusing.

[haughty burrow]

I have just started learning about coterminal angles today and don’t understand it

[shell falcon]

What's the definition of a coterminal angle?

[haughty burrow]

Angle that shares the same terminal side

[shell falcon]

Okay. And what's a way to know when two angles share the same terminal side?

Can you think of one?

[haughty burrow]

When the angle is 360 degrees more than the original or angle or 2 pi more

Maybe

[shell falcon]

No. If we have two arbitrary angles, how can we tell if they're coterminal?

[haughty burrow]

I don’t know to be honest

[shell falcon]

Okay, what does it mean to say that they "share a terminal side"?

[haughty burrow]

Both angles Terminal sides are at the same place but the initial is the same as well

[shell falcon]

Okay, what are "initial" and "terminal" sides?

[haughty burrow]

Initial side is where the angle starts and the terminal side is how much degrees the angle is so from the initial side the terminal side could be say 55 degrees

[shell falcon]

Okay, let's just start from the beginning.

Now, when we talk about angles, it's convenient to talk about them in what we call the "standard position".

That's when we put the angle in the Cartesian plane - the xy plane - such that one side is the x-axis, the origin is the vertex, and the other side is whatever the angle measure is counterclockwise from the first side.

The standard position is absolutely vital for understanding angles.

Two angles are "coterminal" if and only if their terminal sides overlap in standard position.

The "terminal" side being the side that is not (necessarily) overlapping the x-axis.

[haughty burrow]

Ok I understand that part

[shell falcon]

Okay, so.

Supposing that two angles are coterminal, how could we tell?

[haughty burrow]

If they have the same terminal side

[shell falcon]

Okay, let's try it a different way. Are you familiar with trigonometry?

Okay, wait.

No, this might actually work.

[shell falcon]

So how would we tell that?

[haughty burrow]

If they are the same degrees

[shell falcon]

...is it possible for two angles with different measure to be coterminal?

[haughty burrow]

Yes

[shell falcon]

So then that's not the way we can tell if two angles are coterminal.

[haughty burrow]

Ok so how would we tell with radians

[shell falcon]

Okay. Let's think about this. What angles are coterminal with an angle of 0?

[haughty burrow]

Angle between 0 and 2 pi

[shell falcon]

...so any angle between 0 and 2pi is coterminal with an angle of 0?

[haughty burrow]

It has to be 2 pi