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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
328,662,734,008,746,000
Geopchad
01/30/2022 00:05:49
Second you should notice that only some values (so not intervals) work
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
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Geopchad
01/30/2022 00:06:02
You can’t divide by 2 and cancel the inside
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:06:07
You have $1 - f(2x) \le 0$
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
510,789,298,321,096,700
TeXit
01/30/2022 00:06:09
**n/c**
https://cdn.discordapp.c…907677024278.png
739644907677024278.png
0
1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:06:43
Clearly $f(2x) \neq 2f(x)$ because $f$ is not a linear map
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645,687,109,868,585,000
TheCookieMOnster
9431
TheCookieMOnster
false
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
510,789,298,321,096,700
TeXit
01/30/2022 00:06:45
**n/c**
https://cdn.discordapp.c…907677024278.png
739644907677024278.png
0
1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:07:13
So
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:07:28
I can’t divide by 2
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:08:46
Think of a simple example. Is sin(pi/2) = 1/2 sin(pi)?
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:09:22
I don’t know
1
0
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:09:31
That looks more complicated
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:10:13
Just. compute them?
0
1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:10:22
Oh
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:11:12
They’re not equal
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:11:29
Right, so if f(2x) = 2 f(x), then it has to be true for all values of x
0
1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:11:40
You just found a value (x = pi) where they are not equal
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1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:12:10
True
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:12:55
Would I have to use inverse sin?
1
0
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:13:52
Okay, so you have $1 - \sin(2x) \le 0$
0
1
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null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
510,789,298,321,096,700
TeXit
01/30/2022 00:13:54
**n/c**
https://cdn.discordapp.c…907677024278.png
739644907677024278.png
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:13:57
How can you simplify this further?
0
1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:14:21
I can send sin(2x) to the other side
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:14:52
Right, so do that
0
1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:14:58
But then what
1
0
null
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:15:07
If I can’t divide by 2
1
0
null
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:16:28
Think about what sin(anything) can equal
0
1
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:16:35
Maybe draw a graph of sin(x)
0
1
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:18:07
But
1
0
null
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null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:18:21
This one is 1/sin
1
0
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:18:51
We're talking about solving the inequality, aren't we?
0
1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:19:15
I’m trying to find the discontinuities
1
0
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:20:08
Okay, let's take a step back. Why are we solving that inequality?
0
1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:20:36
Because the square root has to be > 0
1
0
null
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:20:57
That is true, and what else? Specifically, what causes a discontinuity?
0
1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:21:57
0 being in the denominator
1
0
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:22:19
Exactly, so right now we're looking at both of those cases.
0
1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:22:27
When is 0 in the denominator?
0
1
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:22:53
When the square root makes a 0
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:24:05
Right, so what equation do we need to solve to see when that happens?
0
1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:24:24
The sin?
1
0
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:24:33
Be specific, write it out here
0
1
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:24:56
Do I need to include the square root in the inequality?
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:25:15
I’m solving for 1-sin(2x)
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:25:36
1-sin(2x)>0
1
0
null
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:26:35
Okay, so you're solving for when it's positive, which also works
0
1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:26:49
So why don't you simplify that inequality
0
1
null
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:26:59
I made it
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:27:09
1 > sin(2x)
1
0
null
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null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:28:16
So actually, let me tell you something I did before
0
1
null
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:28:27
Before, we were solving $1 \le \sin(2x)$
0
1
null
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null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
510,789,298,321,096,700
TeXit
01/30/2022 00:28:29
**n/c**
https://cdn.discordapp.c…907677024278.png
739644907677024278.png
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:28:40
This is because if we solve this inequality, we solve for what we don't want to happen
0
1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:28:54
That is, we don't want the square root to be negative, and we don't want it to be 0
0
1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:29:05
You, on the other hand, are solving for when neither of those things happen
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1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:29:25
But that won't help us with what we're trying to do, because we're trying to find cases where it goes wrong
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1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:29:29
How
1
0
null
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null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:29:38
Should I flip the sign?
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:30:08
Okay, so what happens if sin(2x) = 1?
0
1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:30:21
A zero
1
0
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:30:53
Right, and what happens if sin(2x) > 1?
0
1
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:31:12
It’s continuous
1
0
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:31:25
What do you mean?
0
1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:32:06
There isn’t a discontinuities if sin (2x) is > 1
1
0
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:32:17
Wait
1
0
null
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:32:20
:soynoo:
1
0
null
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:33:07
Doesn’t sin (2x ) have to be < 1
1
0
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:34:34
It does, but I was getting to that
0
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:34:47
My point was if sin(2x) > 1, then the inside of the square root is negative
0
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:34:52
Which is the other case that we don't want
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:35:13
Thus $1 \le \sin(2x)$ covers both cases: denominator being 0, and the inside of the square root being negative
0
1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
510,789,298,321,096,700
TeXit
01/30/2022 00:35:16
**n/c**
https://cdn.discordapp.c…907677024278.png
739644907677024278.png
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:35:32
Ohh
1
0
null
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null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:35:42
Got it
1
0
null
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null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:36:28
But
1
0
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363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:36:50
Now I have 1 >= sin (2x)
1
0
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:37:09
No, you need $1 \le \sin(2x)$
0
1
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
510,789,298,321,096,700
TeXit
01/30/2022 00:37:11
**n/c**
https://cdn.discordapp.c…907677024278.png
739644907677024278.png
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:37:19
No it’s 1 <= sin (2x)
1
0
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help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:37:21
Yea
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:37:37
Now I divide by 2?
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:38:19
Didn't we go over that already?
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:39:47
Oh
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:39:52
So what do I do
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:40:00
I can use the other sin
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:40:09
The inverse sin
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
734,794,827,077,648,600
yes sam
01/30/2022 00:40:57
Would you steal my cookies?
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:41:03
Okay, how about we consider 1 = sin(2x)?
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:41:11
Yes.
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:42:06
Isn’t it going to be 1/2 = sin (x)
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:42:25
I really have no clue what the next step is
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:42:28
:soynoo:
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:43:01
I really suggest reviewing some khan academy algebra videos
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
739,644,907,677,024,300
n/c
01/30/2022 00:43:17
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:43:19
Pls give me a hint
1
0
734,794,827,077,648,600
yes sam
5028
fäf
false
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:43:30
I’ve solved a million problem like this before
1
0
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
261,933,205,387,477,000
riemann
01/30/2022 00:54:15
,w plot y = 1 and y = sin(2x) for -20 < x < 20
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
510,789,298,321,096,700
TeXit
01/30/2022 00:54:33
Results provided by WolframAlpha
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
706,934,233,012,371,600
Ansh_
01/30/2022 00:55:36
:bearlain:
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
706,934,233,012,371,600
Ansh_
01/30/2022 00:56:34
What's the point of discontinuity for this function?
0
1
null
null
null
null
null
363
help-10
4a9d1dcb37364d50bc3d3eb3f28cc741
645,687,109,868,585,000
TheCookieMOnster
01/30/2022 00:58:43
For sin(2x)?
1
0
null
null
null
null
null