Stuck with modulus sign | Mathematics | Page 1

cloud hemlock Jun 17, 2025, 9:07 AM

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I was trying to derive the derivation of arcsec(x). But couldn't conclude why we put |x| in the final solution. Any help would be appreciated.

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zealous currentBOT Jun 17, 2025, 9:07 AM

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cloud hemlock I was trying to derive the derivation of arcsec(x). But couldn't conclude why we...

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celest valve Jun 17, 2025, 9:11 AM

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arcsec outputs in what range?

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@cloud hemlock

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OK you wrote that in there

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Mb

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I will give you a hint

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Bro you made an even huge error

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You wrote tan in terms of x wrong

cloud hemlock Jun 17, 2025, 9:19 AM

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celest valve You wrote tan in terms of x wrong

Oh ignore that, I fixed it later

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The point is the |x| in the final formula

celest valve Jun 17, 2025, 9:19 AM

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It would be $\pm\sqrt{x^{2} - 1}$

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@cloud hemlock

cloud hemlock Jun 17, 2025, 9:21 AM

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Where are u talking about?

celest valve Jun 17, 2025, 9:22 AM

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Bruh

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1 + Tan² = sec²

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Tan = (+ or -)sqrt(sec² -1 )

sand jasperBOT Jun 17, 2025, 9:23 AM

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IdoMeth

celest valve Jun 17, 2025, 9:24 AM

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You wrote only +

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@cloud hemlock

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Then see when negative applies and when positive you will see that it correlates with the sign of x and so you can put modulus instead of (+-)

cloud hemlock Jun 17, 2025, 9:32 AM

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So u mean that the solution is $\frac{1}{|x|\pm\sqrt{x^2-1}}$

sand jasperBOT Jun 17, 2025, 9:32 AM

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SireSirol

celest valve Jun 17, 2025, 9:32 AM

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No

cloud hemlock Jun 17, 2025, 9:32 AM

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@celest valve

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Then?

celest valve Jun 17, 2025, 9:33 AM

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The +- can be converted into modulus

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And that's because tan = sqrt(x²-1) when x is positive and
tan = -sqrt(x²-1) when x negative

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So we can put modulus instead of +- because |x| = x when x>0
And |x| = -x when x<0

cloud hemlock Jun 17, 2025, 9:37 AM

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So what will be it's range?

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The derivative range

celest valve Jun 17, 2025, 9:38 AM

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(-∞, 0) U (0, ∞) for x ∈ (-∞, -1) U (1, ∞) (edit : this is wrong I made a mistake)

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You can plot the graph to find that out

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But did you understand why modulus was put?

celest valve Jun 17, 2025, 9:40 AM

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celest valve And that's because tan = sqrt(x²-1) when x is positive and tan = -sqrt(x²-1) wh...

Do you understand this part?

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You do know that if x² = a then x can be + or - a

cloud hemlock Jun 17, 2025, 9:45 AM

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But the slope of arcsec is always positive if u consider taking the

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Derivative

cloud hemlock Jun 17, 2025, 9:46 AM

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celest valve (-∞, 0) U (0, ∞) for x ∈ (-∞, -1) U (1, ∞) (edit : this is wrong I made a mistak...

I believe the derivative will only give the output between (0, infinity) considering your above explanations

cloud hemlock Jun 17, 2025, 9:47 AM

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celest valve You do know that if x² = a then x can be + or - a

No lol jk

celest valve Jun 17, 2025, 9:47 AM

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cloud hemlock I believe the derivative will only give the output between (0, infinity) consi...

Yeah I could have made mistake in the range let me plot it real quick

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, w plot y = 1/[|x| √(x^2 - 1)]

sand jasperBOT Jun 17, 2025, 9:48 AM

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cloud hemlock Jun 17, 2025, 9:48 AM

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celest valve But did you understand why modulus was put?

Yes, to make the overall derivative positive

cloud hemlock Jun 17, 2025, 9:49 AM

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sand jasper

Interesting

celest valve Jun 17, 2025, 9:49 AM

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cloud hemlock Yes, to make the overall derivative positive

That's true but that's not a proper reason

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We got +- in the answer which we converted into modulus because the sign corelate with sign of x

cloud hemlock Jun 17, 2025, 9:51 AM

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celest valve We got +- in the answer which we converted into modulus because the sign corelat...

Yes, algebraically we can say this

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Thanks for the help

celest valve Jun 17, 2025, 9:52 AM

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Np

cloud hemlock Jun 17, 2025, 9:52 AM

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Our approaches were a little different but we made it to the end.

cloud hemlock Jun 17, 2025, 9:53 AM

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celest valve Np

Where are you from tho?

celest valve Jun 17, 2025, 9:53 AM

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cloud hemlock Where are you from tho?

India

cloud hemlock Jun 17, 2025, 9:53 AM

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celest valve India

Cool, under grad or higschooler?

celest valve Jun 17, 2025, 9:53 AM

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High school

cloud hemlock Jun 17, 2025, 9:53 AM

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12th?

celest valve Jun 17, 2025, 9:54 AM

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Yeah

cloud hemlock Jun 17, 2025, 9:54 AM

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Oh cool, I can sense that u are preparing for JEE

celest valve Jun 17, 2025, 9:54 AM

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Yeah I am

cloud hemlock Jun 17, 2025, 9:55 AM

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celest valve Yeah I am

Alright best of luck, opting for CSE?

celest valve Jun 17, 2025, 9:56 AM

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cloud hemlock Alright best of luck, opting for CSE?

Either CS or MnC

cloud hemlock Jun 17, 2025, 9:57 AM

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celest valve Either CS or MnC

Good luck man

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.close

sonic sequoiaBOT Jun 17, 2025, 9:58 AM

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Unable to parse the channel name

cloud hemlock Jun 17, 2025, 9:58 AM

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Hmm

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@celest valve how do u close

celest valve Jun 17, 2025, 9:58 AM

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+close

wise apexBOT Jun 17, 2025, 9:58 AM

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celest valve +close

You are not authorised to close this help request!

cloud hemlock Jun 17, 2025, 9:59 AM

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+close

wise apexBOT Jun 17, 2025, 9:59 AM

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cloud hemlock +close

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wise apexBOT Jun 17, 2025, 9:59 AM

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wise apex

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#Stuck with modulus sign