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help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:32:00
so both your cases are encapsulated in npi
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Jos11
02/01/2022 10:34:14
I mean shouldn't that look like this instead
https://cdn.discordapp.c…9310/unknown.png
unknown.png
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 10:39:27
@Omegabet_
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:39:41
that's equivalent to npi n in Z
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:39:56
$(2n)\pi$ or $(2n-1)\pi$
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35837029943848f3bd9a89510ec7b642
510,789,298,321,096,700
TeXit
02/01/2022 10:39:58
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 10:43:58
how are they the same tho?
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:44:08
is 2n an integer?
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35837029943848f3bd9a89510ec7b642
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Omegabet_
02/01/2022 10:44:11
yes or no?
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35837029943848f3bd9a89510ec7b642
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Jos11
02/01/2022 10:44:21
no
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:44:30
then your answer was wrong.
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 10:44:38
what
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:44:49
$\sin(t)=0$ means t is an integer multiple of $\pi$
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help-1
35837029943848f3bd9a89510ec7b642
510,789,298,321,096,700
TeXit
02/01/2022 10:44:51
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
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help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:44:59
you just said your answer included non-integer multiples
0
1
837,652,910,794,866,700
謝墨離
3191
謝墨離
false
205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:45:57
Hence your answer to sin(t)=0 was wrong.
0
1
837,652,910,794,866,700
謝墨離
3191
謝墨離
false
205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 10:46:29
so this is incorrect?
1
0
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help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:46:46
yes, as you just said 2n isn't an integer
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help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:47:09
However you also failed to define n in your answer
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 10:48:33
Yeah true, I forgot to do n ∈ Z
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:49:00
so **yes, 2n is an integer**
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 10:49:53
in this context, yes. but it doesn't explain how n2pi=npi
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:50:10
the n I used isn't the same as the one you used..
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:50:33
nowhere did I claim 1=2 as you just suggested
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 10:56:23
https://cdn.discordapp.c…4910/unknown.png
unknown.png
1
0
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help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:56:36
yes
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:56:43
again, **different n's**
0
1
321,445,119,171,756,000
Shuri2060
9525
a μ-er
false
205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 10:56:52
what is that n then
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 10:57:01
i don't understand
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:57:01
**any integer**
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:57:17
$\sin(t)=0\iff t=n\pi, n\in\mathbb{Z}$
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help-1
35837029943848f3bd9a89510ec7b642
510,789,298,321,096,700
TeXit
02/01/2022 10:57:19
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:58:01
To which, if for some reason you want to, you can say t=2npi or (2n-1)pi, n in Z
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 10:58:13
**again, they are different ns**
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:02:26
alright, how do you get that t=npi, n in Z?
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:02:34
graph of sin(t)
0
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:02:42
,w plot y=sin(x)
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help-1
35837029943848f3bd9a89510ec7b642
510,789,298,321,096,700
TeXit
02/01/2022 11:02:44
Results provided by WolframAlpha
0
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:03:04
it has roots at every integer multiple of pi
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:07:12
but without symbolic calculators
1
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:08:54
@Omegabet_
1
0
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null
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help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:09:11
know the graph
0
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:09:14
or the unit circle
0
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:09:35
Like sin(x) is the y component of the circle
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:10:25
thus it's 0 everytime the terminal arm is on the x axis
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:13:30
so hold on, is that the answer to the question?
1
0
321,445,119,171,756,000
Shuri2060
9525
a μ-er
false
205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:13:47
x=npi, n in Z
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:16:15
@gmod
1
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:16:19
oops
1
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:16:23
sorry wrong ping
1
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:16:26
@Omegabet_
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:16:36
no.
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:16:49
That was the answer to my leading question....
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:17:07
.
0
1
null
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help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:17:23
45 minutes ago, when I thought we were done doing sin(t)=0, I said this.
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:26:12
so the answer is this then
https://cdn.discordapp.c…9184/unknown.png
unknown.png
1
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:26:19
isn't it
1
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:26:28
@Omegabet_
1
0
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help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:26:35
probably not but that's what i'd say
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:26:39
No
0
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:26:49
first: does $\sin(x)=\pi$ have a solution?
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help-1
35837029943848f3bd9a89510ec7b642
510,789,298,321,096,700
TeXit
02/01/2022 11:26:52
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
null
null
null
null
205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:28:12
instead of blindly jumping into math, actually think about the question
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:30:05
by this are you referring to the original question or the question you presented?
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:30:15
referring to this
0
1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:30:20
cause this is complete nonsense
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:31:08
You blindly, and horribly, jumped directly into solving sin(x)=2n*pi
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:31:43
which is irrelevant, and then you used n again for the random integer
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:35:25
yes
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:35:37
it does?
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1
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:35:51
Please, enlighten me as to what real number x will make sin(x)=pi
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:36:24
oh yeah, nvm
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:37:16
so does $\sin(x)=n\pi$ have a solution when $n\in\{n\in\mathbb{Z}|n\geq 1\}$?
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help-1
35837029943848f3bd9a89510ec7b642
510,789,298,321,096,700
TeXit
02/01/2022 11:37:19
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
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null
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help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:38:44
what does that last part mean?
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:39:07
n is an integer >= 1.
0
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35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:39:45
alright
1
0
null
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help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:40:25
doesn't have a solution
1
0
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35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:41:21
yes, and for $n\in\{n\in\mathbb{Z}|n\leq -1\}$?
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35837029943848f3bd9a89510ec7b642
510,789,298,321,096,700
TeXit
02/01/2022 11:41:23
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
null
null
null
null
205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:41:30
no
1
0
null
null
null
null
null
205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:41:37
so only n=0 will give solutions.
0
1
null
null
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null
null
205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:41:51
hence $\sin(x)=0$
0
1
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205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:41:52
yeah
1
0
null
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null
205,816
help-1
35837029943848f3bd9a89510ec7b642
510,789,298,321,096,700
TeXit
02/01/2022 11:41:54
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
null
null
null
null
205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:48:27
So is this the answer
https://cdn.discordapp.c…9722/unknown.png
unknown.png
1
0
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205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:49:44
yes.
0
1
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205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:49:57
since you're adamant about writing the answer in 2 different cases
0
1
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205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:52:01
i still don't fully understand the npi thing, so I just do it like that
1
0
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205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:53:37
n is an integer.
0
1
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205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:53:39
end of
0
1
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205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:53:46
which is how my math book does it as well, so I assume it's just smth that I haven't gone through yet (the book is in finnish, don't be confused)
https://cdn.discordapp.c…6374/unknown.png
unknown.png
1
0
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null
205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:53:55
Yeah, that's fine
0
1
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205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:54:02
cause you need to do it that way
0
1
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205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 11:56:03
I don't see how this is fundamentally any different from the question that we just did
1
0
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205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 11:58:45
0 is an exact value
0
1
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205,816
help-1
35837029943848f3bd9a89510ec7b642
186,109,587,366,215,680
Omegabet_
02/01/2022 12:01:44
it's *much* simpler to just write $x=n\pi, n\in\mathbb{Z}$ then continuing to have 2 cases for when n is even and n is odd.
0
1
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205,816
help-1
35837029943848f3bd9a89510ec7b642
510,789,298,321,096,700
TeXit
02/01/2022 12:01:47
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
null
null
null
null
205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 12:06:22
alright I think I understand this now
1
0
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null
205,816
help-1
35837029943848f3bd9a89510ec7b642
360,396,308,344,864,800
Jos11
02/01/2022 12:06:44
but it only applies when the angle is 0, right?
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