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#1 2014-06-16 03:12:39

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

trigonometry

If
gif.latex?f%28x%29%3D3%5Cleft%20%5B%20sin%5E%7B4%7D%5Cleft%20%28%20%5Cfrac%7B3%5Cpi%20%7D%7B2%7D%20%5Cright-x%20%29%20+sin%5E4%5Cleft%20%28%203%5Cpi+x%20%5Cright%20%29%5Cright%20%5D-2%5Cleft%20%5B%20sin%5E6%5Cleft%20%28%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20+x%5Cright%20%29%20+sin%5E6%285%5Cpi-x%29%5Cright%20%5D

then,for all permissible values of x, f(x) is


a)-1
b)0
c)1
d)not a constant function

Last edited by niharika_kumar (2014-06-16 03:16:17)


friendship is tan 90°.

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#2 2014-06-16 03:52:55

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: trigonometry

Hi niharika_kumar


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#3 2014-06-16 06:31:29

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: trigonometry

hi Niharika,

First take out the pi from those trig expressions.

eg.

They all come down to simple trig expressions like this.

You can make use of these:

and

re-arranging these and using them to eliminate the higher powers just leaves an expression with numbers and sin^2 and cos^2.

It is fairly simple from there.

Stefy: I didn't get that answer. ???

Bob


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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#4 2014-06-16 08:00:05

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: trigonometry

Hi Bob

I got the same thing you did, but I am blind. I thought 1 was the a) option. smile


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#5 2014-06-16 20:01:58

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: trigonometry

I thought that was my role.  smile

Bob


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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#6 2014-06-16 22:05:18

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: trigonometry

Well, I guess that, as I get older and you get younger, such things will start to happen.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#7 2014-06-16 23:59:49

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: trigonometry

Stefy wrote:

as I get older and you get younger

Is that happening ?  See you as we pass then.  smile

Bob


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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#8 2014-06-17 00:01:50

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: trigonometry

Wonder when we will be the same age...


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#9 2014-06-17 00:22:09

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: trigonometry

Are we even going at the same speed ?

Bob


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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#10 2014-06-17 00:23:42

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: trigonometry

I have no idea... We should test that somehow.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#11 2014-06-17 00:41:43

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: trigonometry

Measuring time can be tricky.  What do you measure it against ?

I watched a nature program where they filmed some blue math (a common garden bird in the UK) fighting over a bird table.  The fight was all over in a flash and you couldn't really tell what had happened.  But then they slowed the film down by a factor of 10, and there was loads of action; stabs and counter blows; twists and turns in the air.  It was like a one minute wrestling match, but all condensed into less than a second.  It seemed like the birds could think and move ten times quicker.  In another they recorded some bird song and slowed that right down.  Hundreds of notes were made in just a second.  Again it seems the bird was operating in a different time frame from us.  Just as well they haven't got opposable thumbs.

Bob


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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#12 2014-06-17 01:51:18

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: trigonometry

Well, it's not primarily time that's making the matter hard. It's the concept of aging and also the concept of the speed of aging.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#13 2014-06-18 16:21:19

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

Re: trigonometry

got it..
thanks. smile


friendship is tan 90°.

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#14 2014-06-18 16:42:48

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

Re: trigonometry

pls. have a look at this one:-

If


such that

and

then prove that

Last edited by niharika_kumar (2014-06-18 16:43:16)


friendship is tan 90°.

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#15 2014-06-18 19:46:58

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: trigonometry

hi Niharika,

This time I've worked this through all the steps.  smile

When terms add up to zero, you often cannot tell much about them; but when they multiply to make zero, you can.  So this pointed me towards the factor formulas:

and

Now you have three cos terms not two; so which to apply the formula to ?  As term 2 and term 3 are the more complicated, I chose those two.  Similarly for the sin terms.

That will lead you to an opportunity to make cos(gamma/2) as the subject of both, and hence to eliminate it.

I simplified that to

and because of the valid interval (0, pi) you can say

Substituting back leads to alpha = 0 or cos(gamma/2) = 1/2.  The result you want follows.

Bob


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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#16 2014-06-19 15:31:29

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

Re: trigonometry

bob bundy wrote:

Substituting back leads to alpha = 0 or cos(gamma/2) = 1/2. 
Bob

i couldn't get this statement.


friendship is tan 90°.

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#17 2014-06-19 20:01:18

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: trigonometry

hi

You should have got an equation like this:

***

and another similar.

So if beta + gamma/2 = pi:

So use the compound angle formula again to eliminate the pi, factorise cos alpha and the result follows.

Bob

*** If you didn't get this, we need to go back to an earlier step.


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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#18 2014-06-22 02:15:19

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

Re: trigonometry

hmm, thanks. smile


friendship is tan 90°.

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#19 2014-07-04 16:56:04

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

Re: trigonometry

here's another question;

prove that


friendship is tan 90°.

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#20 2014-07-05 00:03:01

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: trigonometry

Let


Then,


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#21 2014-07-05 01:09:51

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

Re: trigonometry

Hi niharika_kumar;

I think you meant

Then you can use the known identities, (halfway down):

http://en.wikipedia.org/wiki/List_of_tr … identities

The rest is simple addition.

Howdy gAr!


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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#22 2014-07-05 03:59:13

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

Re: trigonometry

(silly me.)Yes I meant cos4\theta.
thanks for the correction as well as for the proof.:)


friendship is tan 90°.

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#23 2014-07-17 04:08:49

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

Re: trigonometry

Solve the equation

Last edited by niharika_kumar (2014-07-17 04:20:33)


friendship is tan 90°.

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#24 2014-07-17 04:17:47

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: trigonometry

Are you sure that is the 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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#25 2014-07-17 04:21:47

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

Re: trigonometry

I am sorry, I missed a digit.
Now it is correct.


friendship is tan 90°.

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