# Is 270 degrees considered to be in the 3rd or the 4th quadrant? [Solved!]

**Daniel** 10 Dec 2015, 09:42

### My question

Hi Murray, I have a question about the information provided on the linked page

My question is: is 270 degrees considered to be in the 3rd or the 4th quadrant? (because 270 is midway between 180 and 360, that's why I'm confused.)

Likewise, is 90 degrees considered to be in the first or the second quadrant?

Thanks for clearing up the confusion.

### Relevant page

6. Trigonometric Functions of Any Angle

### What I've done so far

Tried several examples to get it.

X

Hi Murray, I have a question about the information provided on the linked page
My question is: is 270 degrees considered to be in the 3rd or the 4th quadrant? (because 270 is midway between 180 and 360, that's why I'm confused.)
Likewise, is 90 degrees considered to be in the first or the second quadrant?
Thanks for clearing up the confusion.

Relevant page
<a href="/trigonometric-functions/6-trigonometry-functions-any-angle.php">6. Trigonometric Functions of Any Angle</a>
What I've done so far
Tried several examples to get it.

## Re: Is 270 degrees considered to be in the 3rd or the 4th quadrant?

**Newton** 11 Dec 2015, 06:19

Hi Daniel

Actually, for each of those angles that you mentioned, we would say that they are in no particular quadrant. You usually need to do something special for each one.

For example, when considering `tan x`, it is equivalent to `(sin x)/(cos x)`.

At `x = 0°`, `sin x = 0` and `cos x = 1`, so the value of `tan x` is `0`.

However, at `x = 90°`, `cos x = 0`, so the denominator of `tan x` is `0` which is undefined.

You need to treat each of the `90, 180` and `270` cases separately since they are not in any quadrant.

Hope that helps.

X

Hi Daniel
Actually, for each of those angles that you mentioned, we would say that they are in no particular quadrant. You usually need to do something special for each one.
For example, when considering `tan x`, it is equivalent to `(sin x)/(cos x)`.
At `x = 0°`, `sin x = 0` and `cos x = 1`, so the value of `tan x` is `0`.
However, at `x = 90°`, `cos x = 0`, so the denominator of `tan x` is `0` which is undefined.
You need to treat each of the `90, 180` and `270` cases separately since they are not in any quadrant.
Hope that helps.

## Re: Is 270 degrees considered to be in the 3rd or the 4th quadrant?

**Daniel** 12 Dec 2015, 02:42

It does a lot. Thanks

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