Trig Sub | Mathematics | Page 1

zinc harness Oct 3, 2023, 2:57 AM

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Thanks

fallen flumeBOT Oct 3, 2023, 2:57 AM

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wraith glade Oct 3, 2023, 3:01 AM

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You want the denominator to look like 1 - (sin x)^2 inside the square root

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Then you can replace that with (cos x)^2

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You have a 16 instead of a 1, so your target is going to be 16 - 16(sin x)^2, and then you'll be able to common factor the 16.

naive jayBOT Oct 3, 2023, 3:04 AM

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?

wraith glade Oct 3, 2023, 3:05 AM

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Yeah, either works, but you get to choose, so you might as well choose the positive one

zinc harness Oct 3, 2023, 3:05 AM

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I get to choose the sign for the substitution?

wraith glade Oct 3, 2023, 3:06 AM

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you get to choose the entire substitution. You could choose x = 4 cos(theta) too.

cold badge Oct 3, 2023, 3:06 AM

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SOMEONE HELP ME WIFH GEOMETRY

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HURRY PLS

wraith glade Oct 3, 2023, 3:06 AM

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cold badge SOMEONE HELP ME WIFH GEOMETRY

don't interrupt. open your own thread

cold badge Oct 3, 2023, 3:06 AM

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I’m sorry!

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I will make one rn

zinc harness Oct 3, 2023, 3:14 AM

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What’s wrong here? @wraith glade

wraith glade Oct 3, 2023, 3:15 AM

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when you did the substitution, you didn't replace the bounds

zinc harness Oct 3, 2023, 3:34 AM

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Oh, that's right

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Let me start again

zinc harness Oct 3, 2023, 3:54 AM

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@wraith glade

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I think I got the hang of it

wraith glade Oct 3, 2023, 3:57 AM

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Nice. Looks good.

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(It's long and a bit intricate, so I don't guarantee that it's all correct, but the ideas and process are definitely right, and I think the answer is correct.)

zinc harness Oct 3, 2023, 4:03 AM

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wraith glade (It's long and a bit intricate, so I don't guarantee that it's all correct, but ...

I tried being as precise as possible

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Hopefully it's right

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I'm doing another one right now

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But I'm stuck

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wraith glade Oct 3, 2023, 4:04 AM

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convert to sines and cosine

naive jayBOT Oct 3, 2023, 4:07 AM

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?

wraith glade Oct 3, 2023, 4:08 AM

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go to sines and cosines

naive jayBOT Oct 3, 2023, 4:08 AM

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?

wraith glade Oct 3, 2023, 4:08 AM

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yeah

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take a moment and think about this one

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it's not too hard, but it's also not automatic

zinc harness Oct 3, 2023, 4:10 AM

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Derivative of -csc(x)

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Is cot(x)csc(x)

wraith glade Oct 3, 2023, 4:10 AM

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oh

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I forgot

zinc harness Oct 3, 2023, 4:11 AM

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What would've been an alternative to this?

wraith glade Oct 3, 2023, 4:11 AM

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you can sub u = sin(theta), and the cos(theta)d(theta) becomes du

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so it's just integral of 1/u^2 du

zinc harness Oct 3, 2023, 4:11 AM

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O yeah right

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I should get the same result though right

wraith glade Oct 3, 2023, 4:11 AM

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yes

zinc harness Oct 3, 2023, 4:13 AM

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wraith glade yes

I get

naive jayBOT Oct 3, 2023, 4:14 AM

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?

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With $\theta = \atan \frac{e^x}{2}$?

wraith glade Oct 3, 2023, 4:16 AM

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seems good

zinc harness Oct 3, 2023, 4:19 AM

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Isn’t there a way I can rewrite the arctan

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So that I don’t have any trig functions in my final answer

wraith glade Oct 3, 2023, 4:20 AM

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nope

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the (1 + u^2) in the denominator pretty much makes it unavoidable

zinc harness Oct 3, 2023, 4:21 AM

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This is weird though

wraith glade Oct 3, 2023, 4:21 AM

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a little bit, yeah

zinc harness Oct 3, 2023, 4:22 AM

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,w $\int \frac{dx}{e^x\sqrt{4+e^{2x}}}$

naive jayBOT Oct 3, 2023, 4:22 AM

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Results provided by WolframAlpha

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wraith glade Oct 3, 2023, 4:22 AM

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Oh, sorry

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you're taking csc of arctan

zinc harness Oct 3, 2023, 4:23 AM

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I don't know how to use this bot 😭

wraith glade Oct 3, 2023, 4:23 AM

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yeah, draw a triangle

zinc harness Oct 3, 2023, 4:23 AM

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Yeah

wraith glade Oct 3, 2023, 4:23 AM

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sorry, brain fart

zinc harness Oct 3, 2023, 4:24 AM

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Wait, so how should I proceed?

wraith glade Oct 3, 2023, 4:24 AM

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suppose you have cos(arcsin(x))

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you draw a right triangle with opposite x, hypotenuse 1

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because that's what arcsin(x) means

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then you pythagorean theorem and find cos

zinc harness Oct 3, 2023, 5:10 AM

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@wraith glade

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I'm having a tough time

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Can you re-explain please

wraith glade Oct 3, 2023, 5:12 AM

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https://www.youtube.com/watch?v=XZne57aKl58

YouTube

blackpenredpen

cos(arcsinx) as an algebraic expression, cosine of inverse sine x

▶ Play video

zinc harness Oct 3, 2023, 5:22 AM

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wraith glade https://www.youtube.com/watch?v=XZne57aKl58

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What’s the hyp?

zinc harness Oct 3, 2023, 5:44 AM

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This correct?

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Different answer here…

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Do you know where I made my mistake?

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Oh, never mind I got it

zinc harness Oct 3, 2023, 7:23 AM

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Thanks for your help

wraith glade Oct 3, 2023, 11:26 PM

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Great! And you figured out the Pythagorean theorem for the hypotenuse

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If you have no more questions, you can use .solved to close the thread.

zinc harness Oct 4, 2023, 6:01 AM

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Yeah, we’re set

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Thanks

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.solved

#Trig Sub