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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:15:20
its domain is [-1, 1]
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1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:15:27
oh righht
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:15:37
isnt this because it's a function?
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
755,831,671,588,126,700
RepliedPencil
01/29/2022 13:15:47
The output it gives is between that. It accepts inputs from - 1 to 1
0
1
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null
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:15:53
and if ur function has like more than 1 answer at the same y location its not a function
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:15:57
https://cdn.discordapp.c…3238/unknown.png
unknown.png
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:15:59
no?
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:15:59
If this helps.
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:16:02
sin(x) is a function
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:16:08
but its not injective (as shuri said) so we can't invert it
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:16:09
I mean arcisn
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:16:13
you can think of injective as one-to-one
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:16:16
for now
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:16:28
to invert sin(x) we would need it to be one-to-one
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1
617,876,180,011,581,400
body wash
0757
body wash
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205,741
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62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:16:33
so we have to restrict its domain
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:16:40
(which is why we have to add 2pi k to the answer)
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:16:51
$$\sin (x) = \sin(x + 2k\pi)$$
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help-1
62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 13:16:53
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:17:32
$$\sin x \geq \frac{1}{2}$$
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 13:17:35
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:17:35
This is a good one
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:17:38
You asked.
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:18:06
Yea
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:18:09
https://cdn.discordapp.c…9234/unknown.png
unknown.png
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:18:10
how would we solve this
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:18:15
You should expect this answer graphically ok?
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
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Geopchad
01/29/2022 13:18:17
shuri boutta wip out the \bigcup_{n=1}^{\infty} notation 😮
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1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:18:20
Yea
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:18:23
So first we need to figure out where sin x = 1/2
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:18:28
Thats the kindof 'end points'
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:18:29
whenever the sin function reaches above 0.5 that's correct for sin(x)
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:18:48
You solve sin x = 1/2, and then figure out which way round the intervals go
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:18:50
if that makes sense.
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:19:00
(almost everyone would sketch a graph just to check)
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62c1b01245174813bf9d8b6a5a63340c
755,831,671,588,126,700
RepliedPencil
01/29/2022 13:19:18
Pretty much yeah Because sine is a continuous and oscillatory function
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:19:27
ok well ok
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:19:30
this would probably also be easy
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:19:33
when I can just sketch the graph
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:19:39
one more thing
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:19:43
this is a more complicated thing
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:19:50
its from a summer semester exam from like 2014
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:20:02
https://cdn.discordapp.c…6754/unknown.png
unknown.png
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1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:20:06
I was literally unable to solve this
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:20:09
I just couldn't
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:20:12
I couldn't even simplify it
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:20:17
well note that that is a quadratic?
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:20:23
yeah I can replace it with
0
1
null
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:20:28
1/2(1-cos2x) for example
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:20:32
no
0
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794,015,139,581,788,200
caydog
3445
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false
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:20:34
u just let u = sin(x)
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:20:34
It's a quadratic in sin x
0
1
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null
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:20:36
then solve a quadratic
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794,015,139,581,788,200
caydog
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:20:48
was it really that easy
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:20:56
god damn it
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:21:08
It's just something to spot
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Jun♾
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:21:14
Going back to what you asked
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:21:15
The method is:
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:21:16
https://i.imgur.com/Lz5VjwP.png
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1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:21:24
You solve this inequality for 1 period
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:21:26
of sin x
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:21:34
And then extend this by taking this solution every 2pi
0
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62c1b01245174813bf9d8b6a5a63340c
755,831,671,588,126,700
RepliedPencil
01/29/2022 13:21:59
Hence the 2pi k
0
1
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62c1b01245174813bf9d8b6a5a63340c
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lennygo
01/29/2022 13:22:09
is there a way to get the accurate area when its not something easy like pi/2 ?
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:22:10
Between 0 and pi/2, pi/6 is the solution for sin = 0.5
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62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:22:30
between pi/2 and pi, its (pi - pi/6) = 5pi/6
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62c1b01245174813bf9d8b6a5a63340c
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lennygo
01/29/2022 13:22:34
no wait not area
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62c1b01245174813bf9d8b6a5a63340c
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lennygo
01/29/2022 13:22:41
I meant the distance between the area's
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:23:02
What do you mean
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62c1b01245174813bf9d8b6a5a63340c
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lennygo
01/29/2022 13:23:17
If I wanna put this in an answer like my professor does
0
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62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:23:18
If they don't give you easy ratios/angles you're going to have to write it in exact form (or approx with calculator)
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62c1b01245174813bf9d8b6a5a63340c
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lennygo
01/29/2022 13:23:20
how would I do it?
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:23:38
You're talking about this?
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62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:23:40
especially if it was like something like pi/47 I guess
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62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:23:43
yea
0
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help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:23:49
First solve sin x = 1/2
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Jun♾
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62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:23:53
For 0 <= x <= 2pi
0
1
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62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:24:12
x = pi/6 or pi(5/6)
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Jun♾
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62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:24:37
observe from the graph
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:24:52
$$x\in\left[\frac{\pi}{6},\frac{5\pi}{6}\right]$$
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:24:55
wait could I technicall just
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:24:57
In this region
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:25:06
take the middle of the first max of sin
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 13:25:09
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:25:12
?
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:25:25
like theres more than that area right?
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:25:50
wym I don't get you
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:27:06
something like https://cdn.discordapp.com/attachments/269573202018041856/937047265665769593/unknown.png
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:27:08
this but for the area
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:27:10
$$\left\{\frac{\pi}{6}\leq x + 2\pi k\leq\frac{5\pi}{6}, k\in\bZ\right\}$$
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:27:12
instead of single points
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 13:27:38
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:27:44
It would be this.
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:27:47
Inequality.
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:27:49
Not area.
0
1
183,668,144,404,037,630
Ann
0413
Ann
false
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:27:54
It is an interval
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:27:58
oh sorry my bad
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:28:01
I meant interval
0
1
819,818,586,965,016,600
Jun♾
4094
Jun♾
false
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:28:17
$$x + 2\pi k\in\left[\frac{\pi}{6},\frac{5\pi}{6}\right]$$
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 13:28:20
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:28:22
but wouldnt that technicall be wrong if u put 2 for k?
0
1
null
null
null
null
null