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/sci/ - Science & Math

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4693891 No.4693891[STICKY]  [Reply] [Original]

Putnam/Olympiad problem of the day
from http://math.harvard.edu/putnam/

>> No.4693898

>degrees

>> No.4693912

>>4693898
Well....that's just.....you....dude......you saged a sticky !?!?

>> No.4693941

>degrees
it's the gayest putnam problem ever

>> No.4693946
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4693946

>>4693891
>degrees

>> No.4693954

>>4693941
so, this means this sum should work for any reasonably fine subdivision of [0,pi/2], correct?

>> No.4693964

probably need to multiply everything by cos(0)*cos(1)*....*cos(89)
transforming some cos in sin, using cos(a+b)=cos(a)cos(b)-sin(a)sin(b) and almost everuthing should simplify

>> No.4694055

yeah, I'm sure you guys would absolutely slay the problem if it was in rads... fucking losers.

>> No.4694120

<div class="math">-\frac{d}{dt}\csc{t}=\cot{t}\csc{t}=\frac{\cos{t}}{\sin^{2}{t}}</div>

>> No.4694236

>>4693954
Quick check for divisions of pi/4 (1/cos(0)cos(pi/4) = sqrt(2) = cos(pi/4)/sin^2(pi/4)) and pi/6 (1/cos(0)cos(pi/6) + 1/cos(pi/6)cos(pi/3) = 2*sqrt(3) = cos(pi/6)/sin^2(pi/6)).

>> No.4694618

what are the round symbols?

>> No.4694640

>>4694618
hurr

>> No.4695053
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4695053

>>4694120
>using cosec and cot

>> No.4695083

>>4695053
>i'm too dumb to remember a few more names

>> No.4695223

>>4695083
>Constructing auxiliary functions that increase the amount of work required rather than decreasing it

Do you define the cox function for 1/x at the start of every problem?

>> No.4695409

Reported homework thread.

>> No.4695418

itt: 4th graders

>> No.4695447

Everyone in this thread gets a full scholarship to Harvard medical school

>> No.4695495

>>4695409

nigger

>> No.4695698

1/cos1cos2*1/cos88cos99=1/cos1cos2*1/sen1sen2=cos(2-1)/sen1cos1sen2cos2=cos1/sen1cos1sen2cos2
you can do this all the way up to 45

so it'll be 1/cos0cos1+cos1(1/sen1cos1sen2cos2+...+1/sen44cos44sen45cos45)=cos1/sen1^2

>> No.4696377
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4696377

>>4695698
please write this in latex

>> No.4696425

This shit is trivial, it's just inverting a truncated product of Fourier expansions.

You fuckers need to read up.

>> No.4696435

Why would anyone try to sum this series?

Just expand the bottom in a Fourier series, decompose into a partial fraction and show where the series terminates.

>> No.4696956

<span class="math">\sum_{k=0}^{88} \frac{1}{cos(k\frac{180}{\pi })cos((k+1)\frac{180}{\pi })} = \frac{cos(\frac{180}{\pi })}{sin^{2}(\frac{180}{\pi })}[/spoiler]

>> No.4697750

>>4696956
Other way around; pi/180

>> No.4697981

So...
Did anyone actually solve this?

>> No.4698046

>>4697981
If they have, they haven't posted it.

>> No.4698613
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4698613

>mfw this hasn't been solved

Yes I'm bumping this. U mad?

>> No.4698637

>>4698613
I guess no one just bothered to post any solution since the problem is rather simple.

>> No.4698658

How can you have cos 0? Isn't that like dividing by zero? Are you guys sure OP didn't make this up?

>> No.4698672

>>4698658
Either fail troll or retarded.

>> No.4698674

>>4698658
lel