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#1 2014-04-17 04:26:35

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,028

trigonometry#2

If exp.

satisfies the equation
, find the values of
,

Last edited by niharika_kumar (2014-04-17 04:30:40)


friendship is tan 90°.

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#2 2014-04-17 04:34:24

niharika_kumar
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From: Numeraland
Registered: 2013-02-12
Posts: 1,028

Re: trigonometry#2

I am not able to correct my latex code. It is not coming out properly.I wrote the following code:-

{(sin^2x+sin^4x+sin^6x+......+∞)log_e3}

x is not the part of the exponent.


friendship is tan 90°.

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#3 2014-04-17 04:42:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: trigonometry#2

Hi;

I have adjusted it for you.

You can use

http://www.codecogs.com/latex/eqneditor.php

for all your latex.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#4 2014-04-17 15:54:34

niharika_kumar
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From: Numeraland
Registered: 2013-02-12
Posts: 1,028

Re: trigonometry#2

thanks for editing it.:)
Now i want some help in this question.


friendship is tan 90°.

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#5 2014-04-17 16:31:47

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: trigonometry#2

I do not even get what it means...

Is that a Class XI level problem?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#6 2014-04-17 16:44:16

niharika_kumar
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From: Numeraland
Registered: 2013-02-12
Posts: 1,028

Re: trigonometry#2

yes. And even I don't get what it means.


friendship is tan 90°.

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#7 2014-04-17 17:11:01

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: trigonometry#2

Tip: Log base e (x) is better written as ln(x)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#8 2014-04-17 19:42:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: trigonometry#2

The sum can be handled but is a little tough to prove.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#9 2014-04-17 23:53:42

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: trigonometry#2

niharika_kumar wrote:

If exp.

satisfies the equation

Does it mean:

If

then 

???

What is exp.?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#10 2014-04-18 00:20:51

gourish
Member
Registered: 2013-05-28
Posts: 143

Re: trigonometry#2

i presume that the first part is just not necessary since we get to find the value of x from the quadratic equation as 1 or 27 then probably put it in the cos x over cos x + sin x part to get it's value obviously it will give two values but that's for an amateur like me if somebody can just find the answer to (sin^2 x + sin^4 x+.......) series i might get better ideas to solve it.


"The man was just too bored so he invented maths for fun"
-some wise guy

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#11 2014-04-18 02:11:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: trigonometry#2

Hi;


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#12 2014-04-18 07:13:12

zetafunc.
Guest

Re: trigonometry#2

Agnishom wrote:
niharika_kumar wrote:

If exp.

satisfies the equation

Does it mean:

If

then 

???

What is exp.?

The way the question seems too be worded, one would presume the OP wants to find a θ such that:

and

The sum is trivial (a geometric series), and the quadratic also factorises nicely -- then, you just need to re-write cosθ / (sinθ + cosθ) in terms of tanθ, and you're done.

#13 2014-04-18 16:28:21

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,028

Re: trigonometry#2

exp. means:-

e^{(sin^2x+sin^4x+sin^6x+......+∞)log_e3}

using GP, the sum of (sin^2x+sin^4x+sin^6x+......+∞) comes to be tan^2x

now if we get the value of tan^2x , we can easily get the required value.

Now how to get the value of tan^2x?

and what does In(x) means??

Last edited by niharika_kumar (2014-04-18 16:30:51)


friendship is tan 90°.

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#14 2014-04-18 21:05:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: trigonometry#2

ln(x) is the number that e must be raised up to, to get x.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#15 2014-04-19 02:10:06

zetafunc.
Guest

Re: trigonometry#2

niharika_kumar wrote:

exp. means:-

e^{(sin^2x+sin^4x+sin^6x+......+∞)log_e3}

using GP, the sum of (sin^2x+sin^4x+sin^6x+......+∞) comes to be tan^2x

now if we get the value of tan^2x , we can easily get the required value.

Now how to get the value of tan^2x?

and what does In(x) means??

ln(x) is a notation often used in place of log base e.

#16 2014-04-19 18:23:55

gourish
Member
Registered: 2013-05-28
Posts: 143

Re: trigonometry#2

well x is either 1 o 27 put that in for e^x=3*tan^2(x) if x is 1 e=3.tan^2(1) {i don't know if that's right value } and then do the same for x=27 maybe then we can check which of these satisfy the condition. but can we do it in a simpler way cause i don't e^27 or tan^2(1)
tan^2(27) so help needed here....


"The man was just too bored so he invented maths for fun"
-some wise guy

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#17 2014-04-19 19:14:16

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,028

Re: trigonometry#2

still couldn't get it.


friendship is tan 90°.

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#18 2014-04-20 02:49:23

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,532

Re: trigonometry#2

hi

Post 12 shows what this problem is asking.

exp is an alternative notation for e to the power of ....

And lnx is the inverse function to exp.

The quadratic has two solutions: 1 and 27.

The sine series is  geometric with first term sin squared and common ratio also sin squared.

As sin squared is less than 1, you can use the sum to infinity formula to sum this.

So either

(i)

ln 1 is the power you have to raise e to, in order to get 1.  ie. zero.

=> theta = zero but we are told theta is > 0, so this leads to no solutions for theta.

(ii)

so

and

This can be 'rationalised' to

Bob

Last edited by bob bundy (2014-04-20 02:52:46)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#19 2014-04-20 03:08:45

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,028

Re: trigonometry#2

bob bundy wrote:

(ii)

I am a beginner in logarithms, so i couldn't get this part.
Now its clear.

thanks. smile


friendship is tan 90°.

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