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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:03:09
the set of all angles that are in the form of pi / 2 + 2pi * k
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:03:12
We're not done here.
0
1
null
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null
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null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:03:28
oh
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:03:49
wel llennygo
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:03:55
to get all the angles that would make the condition true
0
1
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null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:04:07
you have to first all of the base angles (that is, the ones that are <= 2pi)
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 13:04:10
You're adding a full revolution to 90, so you're getting to the same final angle
0
1
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null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:04:12
then you have to add 2pi * k to each of those options
0
1
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null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 13:05:12
pi/2 + 2pin
0
1
null
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null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:05:30
alright yeah I get
0
1
null
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null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:05:32
If I was writing a proof
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:05:33
$$\sin(x)\geq \cos\left(x+\frac{\pi}{2}\right)+2$$ $\iff$ $$\sin(x)\geq -\sin(x)+2$$ $\iff$ $$\sin(x)\geq 1$$ $\iff$ (because $(\forall x\in\bR)(-1\leq\sin x\leq1)$) $$1\geq\sin(x)\geq 1$$ $\iff$ $$\sin(x) = 1$$
0
1
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:05:36
so in simple terms
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:05:45
if I get to sin(x)=1
0
1
null
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null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 13:05:48
**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 13:05:49
do arcsin of 1
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:05:54
graph sin on the side
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:06:09
arcsin has a specific range.
0
1
null
null
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null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:06:10
check for all answers =>1
0
1
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null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 13:06:16
Why are you doing this?
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
755,831,671,588,126,700
RepliedPencil
01/29/2022 13:06:23
Yes
0
1
null
null
null
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null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 13:06:24
Isn't this where we reached?
0
1
null
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null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:06:26
Im guessing thats mathematically entirely correct
0
1
null
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null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:06:38
I'm saying this is the steps to reach sin x = 1. **but we're not done here**
0
1
null
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null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:06:58
To solve sin x = 1, you do the usual.
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 13:07:07
I think he understands
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:07:14
arcsin both sides and then note the ranges, etc.
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:07:21
Or observe the answer from the graph
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:07:34
Both lead to whats written here
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:07:34
https://cdn.discordapp.c…5022/unknown.png
unknown.png
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:07:35
Oh yeah I understand that arcsin is limited
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:07:49
but still when I apply it
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:07:53
I get one answer
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:07:56
or maybe 2 if its not the max
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:07:59
???
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:08:01
What do you mean.
0
1
null
null
null
null
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:08:08
$$x^2 = 1$$
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 13:08:11
**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 13:08:19
$x = \sqrt{1}$ ???
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:08:20
sin(x)=1 | arcsin x=1/2pi
0
1
263,378,155,140,677,630
Schtew
1564
Schtew
false
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 13:08:21
**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 13:08:43
or x=-1/2pi
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:08:51
uh
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 13:09:03
What
0
1
263,378,155,140,677,630
Schtew
1564
Schtew
false
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:09:04
I am pointing out that the square root function is not a true inverse to f(x) = x^2
0
1
null
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null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
348,696,743,388,381,200
A Lonely Bean
01/29/2022 13:09:08
sin(-pi/2) is definitely not 1
1
0
200,013,547,491,688,450
a disappointing son
0540
a disappointing son
false
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:09:09
because x^2 is not invertible.
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
348,696,743,388,381,200
A Lonely Bean
01/29/2022 13:09:15
If we're still on solving sinx = 1
1
0
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:09:21
The same principle applies to sin.
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:09:26
Sin is not an invertible function.
0
1
null
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null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:09:29
Because it is not injective.
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:09:43
If we want to find **all solutions** to sin x = 1
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:09:47
We need to take this into account.
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:09:56
I think ur blowing it a bit out of the water
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:10:08
I understand what ur saying is probably entirely mathematically correct
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:10:09
https://cdn.discordapp.c…6116/unknown.png
unknown.png
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:10:24
https://cdn.discordapp.c…6246/unknown.png
unknown.png
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:10:27
but I mean I just need the quick answer
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:10:31
You are looking for the green line
0
1
200,013,547,491,688,450
a disappointing son
0540
a disappointing son
false
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:10:50
The quick answer is you need to realise what the range of the arcsin function is to solve the question
0
1
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null
null
null
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 13:10:51
Quick answer?
0
1
657,340,498,788,483,100
Jay_P
8879
Jay_P
false
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:11:05
Ok wait hold on
0
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:11:06
can I just
0
1
null
null
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null
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:11:12
post my entire work
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:11:15
arcsin(1) = pi/2
0
1
null
null
null
null
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:11:16
and you can just tell me if its wrong or not
0
1
530,116,068,644,225,000
aD
0030
aD
false
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:11:17
https://cdn.discordapp.c…9593/unknown.png
unknown.png
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:11:25
And you take this answer mod 2pi ?
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:12:16
https://cdn.discordapp.c…71028/image0.jpg
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:12:20
this is what I would do
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:12:38
that's the teachers work?
0
1
null
null
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:12:41
mine
0
1
null
null
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null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:12:49
well you have the right answer?
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1
530,116,068,644,225,000
aD
0030
aD
false
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:12:53
so whats ur questoin
0
1
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205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:13:07
idk Shuri is telling me probably something important to remember
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:13:15
but I'm not entirely understanding it
0
1
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null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:13:17
all shuri is saying is that you have to add 2pi k
0
1
null
null
null
null
null
205,741
help-1
62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:13:17
Your working is fine.
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62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:13:27
beacuse the arcsin only returns one of the infinite angles
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62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:13:36
oh yeah I understand that concept
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62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:13:39
https://cdn.discordapp.c…5633/unknown.png
unknown.png
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62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:13:45
it's only defined till 2pi i think right?
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62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:13:46
(because we have to restrict the sin wave to invert it, as shuri said the whole thing is not "one to one")
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62c1b01245174813bf9d8b6a5a63340c
755,831,671,588,126,700
RepliedPencil
01/29/2022 13:13:47
It has infinitely many solutions, hence the 2pi k
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62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:13:57
I wasn't sure what we were stuck on lol
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62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:14:00
I assumed it was this
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62c1b01245174813bf9d8b6a5a63340c
321,445,119,171,756,000
Shuri2060
01/29/2022 13:14:01
or the inequality
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62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:14:18
what would happen btw if lets just say
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62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:14:19
it was
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:14:23
$\sin^{-1}(x): [-1, 1] \to [-\frac{\pi}{2}, \frac{\pi}{2}]$
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62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:14:25
sin(x)>=0.5
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62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 13:14:26
**M.E.G. Yottachad**
https://cdn.discordapp.c…734008745984.png
328662734008745984.png
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62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:14:49
it only returns values from [-pi/2 to pi/2
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help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 13:14:51
Then there would be a range of x values
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:14:52
but we know there are infinite answers
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:14:55
so we add 2pi k
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:15:05
**note that arcsin is surjective onto [-pi/2, pi/2]
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62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 13:15:09
oh ok so arcsin is just defined from -pi/2 to pi/
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62c1b01245174813bf9d8b6a5a63340c
348,696,743,388,381,200
A Lonely Bean
01/29/2022 13:15:10
Unless solving for 0's
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 13:15:17
no arcsin's range is that
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