Finding Coterminal Angles in Trigonometry

[LordofDirT]

Hey, I've come back for some more help.

This time I have a problem that I believe is easy, but I want to check my answer with you (since there missing in the back of the book) and make sure my notation is correct since I've never taken trig, and class hasn't started yet. So my ramble ends.

If a possitive angle has measure $$x^o$$ between $$0^o$$ and $$60^o$$ how can I represent the first negative angle coterminal with it?

First I drew a diagram to solve it with x as the variable for the positive rotation, and y for the variable for negative rotation. Assuming that they want the measure of the negative angle coterminal (which would be the end of rotation in the negative direction?). So I figured that:

$$180^o + 180^o - x^o = y^o$$

$$360^o - x^o = y^o$$

First of all how correct is this?

And is this the right way to measure the "first" negative angle coterminal?

Is there a second. This is where I'm lost.

 

[Tedjn]

You have the right magnitude for y, but it should be negative, no? In general, how many degrees must be between two coterminal angles? By first negative, it probably refers to the negative angle with the smallest absolute value that is coterminal to x.

 

[LordofDirT]

Oh ok... I get that, since I need to describe the rotation's direction it should be negative.

$$-360^o + x^o = y^o$$


"how many degrees must be between two coterminal angles?"

?

"By first negative, it probably refers to the negative angle with the smallest absolute value that is coterminal to x."

Here I'm lost again. But you've peaked my curiosity...

 

[Tedjn]

What does it mean for two angles to be coterminal?

 

[LordofDirT]

OK, i guess i didn't think of the possibility of rotations above or below 360 degrees. So there could be an infinite number of coterminal angles both positive and negative. So would it be correct to say that a coterminal angle is an angle of the opposite rotation where the coterminal side is in the same position as the first angles terminal side?

 

[Tedjn]

Yes, there are an infinite number of coterminal angles, all differing by 360 degrees ($2\pi$ radians). Coterminal angles don't have to be of the opposite rotation; they just need to have their terminal sides in the same position.

 

[LordofDirT]

Thanks Tedjn!