Inverse trigo | Mathematics | Page 1

fading shard May 16, 2024, 6:34 PM

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I made cases but couldnt really match my answer

pliant brookBOT May 16, 2024, 6:34 PM

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fading shard I made cases but couldnt really match my answer

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sturdy solar May 16, 2024, 6:36 PM

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fading shard I made cases but couldnt really match my answer

What's in the input for arctan?

fading shard May 16, 2024, 6:36 PM

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its from -3 to 3

sturdy solar May 16, 2024, 6:37 PM

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...no.

fading shard May 16, 2024, 6:37 PM

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how

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like not included

sturdy solar May 16, 2024, 6:37 PM

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Because "from -3 to 3" isn't the expression inside of arctan.

fading shard May 16, 2024, 6:37 PM

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wdym by arc tan

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inverse?

sturdy solar May 16, 2024, 6:37 PM

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Inverse tangent, also known as arctangent.

fading shard May 16, 2024, 6:37 PM

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oh

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bro its given in the end

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0<|y|<3

sturdy solar May 16, 2024, 6:38 PM

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That is not the expression inside of arctan.

fading shard May 16, 2024, 6:38 PM

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im talkkin about y

sturdy solar May 16, 2024, 6:39 PM

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I know you are. I don't know why, because I'm not.

fading shard May 16, 2024, 6:39 PM

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😭

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bruh

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the input right

sturdy solar May 16, 2024, 6:39 PM

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Of arctan.

fading shard May 16, 2024, 6:39 PM

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sturdy solar May 16, 2024, 6:40 PM

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Right.

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And what's the input of arccot?

fading shard May 16, 2024, 6:40 PM

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reciprocal of that

sturdy solar May 16, 2024, 6:40 PM

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Right. So what does that mean?

fading shard May 16, 2024, 6:41 PM

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need to make cases...

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They both belonga to different range so i guess we need to make cases

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before converting cot to tan

sturdy solar May 16, 2024, 6:42 PM

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Okay. So make the cases.

fading shard May 16, 2024, 6:42 PM

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I did

sturdy solar May 16, 2024, 6:42 PM

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And what are they? In terms of 6y/(9 - y^2)?

fading shard May 16, 2024, 6:43 PM

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like

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when

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y is +ve

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we can reci[rpcal that

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but if -ve

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oh wait im confused over -ve

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its gonna pie + ?

sturdy solar May 16, 2024, 6:47 PM

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Look. Let x = 6y/(9 - y^2). Then what we have is arctan(x) + arccot(1/x).

fading shard May 16, 2024, 6:48 PM

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right

sturdy solar May 16, 2024, 6:49 PM

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So you're correct that we split it into cases x > 0 and x < 0.

fading shard May 16, 2024, 6:49 PM

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yeah

sturdy solar May 16, 2024, 6:50 PM

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Let's consider - wait, have you studied calculus at all?

fading shard May 16, 2024, 6:50 PM

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yes

sturdy solar May 16, 2024, 6:50 PM

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Okay, so I can talk about limits.

fading shard May 16, 2024, 6:50 PM

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yeah

sturdy solar May 16, 2024, 6:50 PM

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What's the limit as x approaches 0 from below of arccot(1/x)?

fading shard May 16, 2024, 6:51 PM

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idk havent dont limits on inverse yet

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ig 0 tho

sturdy solar May 16, 2024, 6:52 PM

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No.

fading shard May 16, 2024, 6:52 PM

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okay

sturdy solar May 16, 2024, 6:53 PM

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The limit as x approaches 0 from below of 1/x is negative infinity, right?

fading shard May 16, 2024, 6:54 PM

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wait

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you sure

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wont it depend

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ig thats infinity

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like shouldnt that be 0-

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I have to go rn gonna come tomorrow again thanks for the help tho

sturdy solar May 16, 2024, 6:58 PM

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fading shard like shouldnt that be 0-

...I said that. 0 from below.

fading shard May 16, 2024, 7:03 PM

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sturdy solar ...I said that. 0 from below.

yea that should be -ve infinity

sturdy solar May 16, 2024, 7:03 PM

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Right. So it's the limit as u goes to minus infinity of arccot(u).

#Inverse trigo