trigonometry

niharika_kumar · 2014-06-16 03:12:39

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)

anonimnystefy · 2014-06-16 03:52:55

Hi niharika_kumar

Bob · 2014-06-16 06:31:29

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

anonimnystefy · 2014-06-16 08:00:05

Hi Bob

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

Bob · 2014-06-16 20:01:58

I thought that was my role.

Bob

anonimnystefy · 2014-06-16 22:05:18

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

Bob · 2014-06-16 23:59:49

Stefy wrote:

as I get older and you get younger

Is that happening ? See you as we pass then.

Bob

anonimnystefy · 2014-06-17 00:01:50

Wonder when we will be the same age...

Bob · 2014-06-17 00:22:09

Are we even going at the same speed ?

Bob

anonimnystefy · 2014-06-17 00:23:42

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

Bob · 2014-06-17 00:41:43

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

anonimnystefy · 2014-06-17 01:51:18

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.

niharika_kumar · 2014-06-18 16:21:19

got it..
thanks.

niharika_kumar · 2014-06-18 16:42:48

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)

Bob · 2014-06-18 19:46:58

hi Niharika,

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

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

niharika_kumar · 2014-06-19 15:31:29

bob bundy wrote:

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

i couldn't get this statement.

Bob · 2014-06-19 20:01:18

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.

niharika_kumar · 2014-06-22 02:15:19

hmm, thanks.

niharika_kumar · 2014-07-04 16:56:04

here's another question;

prove that

gAr · 2014-07-05 00:03:01

Let

Then,

bobbym · 2014-07-05 01:09:51

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!

niharika_kumar · 2014-07-05 03:59:13

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

niharika_kumar · 2014-07-17 04:08:49

Solve the equation

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

Agnishom · 2014-07-17 04:17:47

Are you sure that is the problem?

niharika_kumar · 2014-07-17 04:21:47

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

Math Is Fun Forum

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

trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

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

Re: trigonometry

#25 2014-07-17 04:21:47

Re: trigonometry

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