Question

How would you find arctan(-1)?

Answer 1

do you have a unit circle diagram with you?

Answer 2

yes

Answer 3

Know the range of arctan, -pi/2 to pi/2, so the answer is -pi/4

Answer 4

ok can you tell me where both sine and cosine are equal...but are different in sign

Answer 5

3pi/4

Answer 6

wrong

Answer 7

that's correct

Answer 8

3pi/4 is out of the range for arctan

Answer 9

tan(3pi/4) = -1

Answer 10

It's -pi/4

Answer 11

are there any other points where sine and cosine are equal, but opposite in sign?

Answer 12

7pi/4

Answer 13

that's coterminal to -pi/4 because you can subtract 2pi from 7pi/4 to get

7pi/4 - 2pi

7pi/4 - 8pi/4

(7pi - 8pi)/4

-pi/4

Answer 14

So the two angles -pi/4 and 7pi/4 are coterminal, ie they lie in the same position (one is just full rotation away from the other)

Answer 15

But you see, there's range for arctan which is from -90 to 90

Answer 16

yes I'm getting there rman3

Answer 17

it turns out that arctan is a function

so you should get EXACTLY ONE output for any given input

since tan(x) = -1 has at least two solutions (there's actually infinitely many of them), we need to come up with a way to pinpoint the value of x when we say x = arctan(-1)

The convention is to restrict the range of arctan to be -pi/4 <= y <= pi/4 which guarantees we only get one output for any given input

Answer 18

-pi/2 <= y <= pi/2 is the range I meant*

Answer 19

anyways, this is why arctan(-1) = -pi/4

in terms of degrees, arctan(-1) = -45 degrees

Answer 20

Well if you let arctan graph go on forever, it becomes not a function so it is restricted from -pi/2 to pi/2

Answer 21

In my mathematics class, my teacher told us that -45 was a wrong answer. He ended up with 135

Answer 22

looks like he added 180 degrees to -45 to get 135

he probably has a reason for doing that, but not sure

Answer 23

I see

Answer 24

it turns out that all solutions of tan(x) = -1 are separated by 180 degrees, so it's not a coincidence. I'm just not sure why your teacher didn't go with -45

maybe he wanted the first positive solution

Answer 25

first positive solution of tan(x) = -1

Answer 26

yeah, tan of 135 = -1, but if that were the case, should it not equal 135 backwards?
ex) tan 135 = -1 but arctan -1 = -45

Answer 27

or am I just mixing up the definition of arctan itself?

Answer 28

by definition, the range of arctan is -90 <= y <= 90

so you saying arctan(-1) = -45 is correct

Answer 29

I'm thinking there's more to the problem than just arctan(-1) though

Answer 30

the full question is:
x=arctan (-1)

Answer 31

so, thanks anyways!
:D

Answer 32

well then unfortunately your teacher is using arctan wrong if that's all there is

Answer 33

Its a possibility that he is looking for a positive angle instead of a negative one.

Answer 34

true, that's always a possibility

and it could be the possibility that he just wants one x value to satisfy tan(x) = -1 and wants that x value to be positive

Answer 35

probably, because -45 also satisfies the equation.

Answer 36

I have to leave, because I need to study other topics, but you should know how grateful I am for your help
Thank you.

Answer 37

you're welcome