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

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

### 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
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

### 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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: trigonometry#2

Hi;

I have adjusted it for you.

You can use

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

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

### 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: Riemann Sphere
Registered: 2011-01-29
Posts: 24,850
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'
I'm not crazy, my mother had me tested.

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

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

### 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
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,850
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'
I'm not crazy, my mother had me tested.

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,850
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'
I'm not crazy, my mother had me tested.

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

gourish
Member
Registered: 2013-05-28
Posts: 153

### 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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: trigonometry#2

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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: 1,062

### 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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #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: 153

### 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: 1,062

### 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
Registered: 2010-06-20
Posts: 8,321

### 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)

Children are not defined by school ...........The Fonz
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: 1,062

### Re: trigonometry#2

bob bundy wrote:

(ii)

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

thanks.

friendship is tan 90°.

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