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The Mathematics Club ~ *ΜΑΘ* ~

Dude22376 said:
Arcsin is the inverse function of sin, you might have seen it written as sin^-1.
e.g. sin pi/2 = 1, so arcsin 1 = pi/2.
Note that the range of arcsin x is -pi/2 to pi/2, so arcsin 1 = pi/2 and not, say, 5 pi/2 (even though sin 5 pi/2 = 1)

For me, instead of turning t back into x, I changed the limits and evaluated based on t:

Let x = sin t.
dx/dt = cos t
dx = cos t dt

First we change the upper and lower limits from x to t. arcsin 0 = 0 and arcsin 1 = pi/2.

[PokeCommunity.com] The Mathematics Club ~ *ΜΑΘ* ~

[PokeCommunity.com] The Mathematics Club ~ *ΜΑΘ* ~

[PokeCommunity.com] The Mathematics Club ~ *ΜΑΘ* ~

[PokeCommunity.com] The Mathematics Club ~ *ΜΑΘ* ~

[PokeCommunity.com] The Mathematics Club ~ *ΜΑΘ* ~

[PokeCommunity.com] The Mathematics Club ~ *ΜΑΘ* ~

= 0 - 0 + pi - 0
= pi

PROTIP
If you see sqrt(a^2-x^2), try to sub in x = a sin t.
For sqrt(x^2-a^2), sub in x = a sec t.
For sqrt(a^2+x^2), sub in x = a tan t.

@Drakow: Nitpicking here. It's incorrect to use 1 and 0 as the upper/lower limits after subbing x for t. You must either change the limits (as I did), or start off with the indefinite integral for x so that you don't need to write the limits for t.
Click to expand...

What you say is true, however, because the substitution reverts back to x anyway, I did not bother changing the limits just to change them back to the original limits. Though you are right, I am mathematically wrong. Anyway, I think your solution is probably the one he was expected to give for his exam.
 
Last edited:
^Dude! I implied that to you in my earlier message when I gave you the property you needed.

Ah, we all make these mistakes. I doubt you'll ever forget that again lol.
 
I've always loved Math, so I would love to be a Full-Pledge Member here :)
I hate how school policies can only hold me back from my potential :(

Username: Lifes-A-Beach
Overall Education Level: 9th Grade (USA)
Mathematics Education Level (Or most recent/advanced math subject): Algebra II / Trigonometry H (School), Pre-Calculus (Independently)
Do you think you can be asked for help in your level or lower?: No (Unfortunately, I don't have much spare time on top of all my other Honors Courses :( )
Life = The Universe = Everything = : 42 is never wrong
 
ATTENTION ALL YOCTOGRAMS!

[PokeCommunity.com] The Mathematics Club ~ *ΜΑΘ* ~


Make Sho Minamimoto your club mascot! You won't regret it for one millisecond!

Username: Sho Minamimoto Bela
Overall Education Level: Undergraduate
Mathematics Education Level (Or most recent/advanced math subject): Most recent math class is a Finite Math hodgepodge class for transfer credit. Crunch! I'll add it to the heap (of credits I have!)
Do you think you can be asked for help in your level or lower?: Let's see the limit of U as I go to infinity!
Life = The Universe = Everything = 3 is the point of the 1. 4 the 1-5-9 are 2. 6-5, 3-5! 8-9, 7-9! 32384 62643 38327! And...perfect.
 
Full pledged Membership for me too =)
Username: Renii
Overall Education Level: About to finish high school. =)
Mathematics Education Level (Or most recent/advanced math subject): Calculus, I think.
Do you think you can be asked for help in your level or lower?: Yeah. I think so.
Life = The Universe = Everything = : Forty twoooooiooo
 
LIST UPDATED! CHEESEUS SWISS CHRIST STOP BUGGING ME! ;_;

Drakow said:
What did the constipated Mathematician do to solve his/her problem?
Click to expand...

I only revived the club because I wanted to hear the end of this one.
 
Renii said:
S/He works it out with a pencil... =_=

Meh, this place is *dead*...
Click to expand...

Beautiful. Let's talk about APs and finals.

So I'm nervouse about my AP Cal result. My principle is being a dick and says if I don't get a 5, I can't skip Cal AB. Sonofagun test felt like a 4. At least I'll also be taking AP stats next year. 4 APs my Sophomore year, I feel brave and insane.

Oh, I also took the liberty of updating everyone's membership to their next logical grade level and math level.
 
What are APs? And a 5, cal AB O.o

I live in a different country, we have a totally different education system.
 
Renii said:
What are APs? And a 5, cal AB O.o

I live in a different country, we have a totally different education system.
Click to expand...

APs = Advanced Placement tests/courses (depending on context), brought to you by the same guys who dish out the SATs. And yes, you've heard about those rare 5's on the Calculus AB tests? Not even MIT is punk enough to demand a 5 on that test, just a 4.
 
Renii is correct.

Hey! You need to add me to the list of fully pledged Mathematicians! Fine . . . I'll fill your form out..

Username: Drakow
Overall Education Level: Finished undergraduate.
Mathematics Education Level - BSc Mathematics - First Class
Do you think you can be asked for help in your level or lower?: If anyone needs help, feel free to drop me a line and I'll do the best I can to sort things out.
 
Username: Masters Cage

Overall Education Level: Year 10 in High School

Mathematics Education Level (Or most recent/advanced math subject): Top class for Maths, never failed a Maths test, doing the hardest Maths course next year at school and TAFE (Maths 2-Unit and Extended Maths)
Do you think you can be asked for help in your level or lower?: Hell Yeah, I get asked about Maths all day at school....

And before you all ask, No.... I'm not a nerd, I play sports and other stuff, it just so happens I'm really good at Maths for a 16 year old....
 
It's exactly been 30 days. Hope I'm not breaking the rules. (Since it said... more than 30 days. :P)

Anyway. Just checking, with only the data given, is it possible to solve this problem... at all? o.o

Let Chords AB and CD of Circle O intersect at Point E. BE=x, EA=3x-1, DE=x-1, CE=4x. Find the lengths of AB and CD.

The way I see it, only in terms of x... right?
 
smile! said:
It's exactly been 30 days. Hope I'm not breaking the rules. (Since it said... more than 30 days. :P)

Anyway. Just checking, with only the data given, is it possible to solve this problem... at all? o.o

Let Chords AB and CD of Circle O intersect at Point E. BE=x, EA=3x-1, DE=x-1, CE=4x. Find the lengths of AB and CD.

The way I see it, only in terms of x... right?
Click to expand...
Read this https://en.wikipedia.org/wiki/Cyclic_quadrilateral#Diagonals and you'll get x = 3

:P
 
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