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#1 2013-07-23 21:20:43

debjit625
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Trigonometric equation problem...

Hi

I know that

1) The general solution for



is

     


And
2) The general solution for



is

     


Now my question is, in an equation like



,which way should I select i.e.. its in both the forms



and



in that case we rewrite the equation




Thanks smile

Last edited by debjit625 (2013-07-23 21:22:56)


Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

#2 2013-07-23 22:11:39

bob bundy
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Re: Trigonometric equation problem...

hi debjit625

My preferred method is to find one solution and then use the cyclical nature of cosine to generate all the others.

There will be two solutions between 0 and 2pi for 2 theta; one in the first and one in the fourth quadrant ( or second and third depending on sign)

Then add all multiples of 2 pi (by adding 2npi)   Sometimes I sketch the cosine graph, just to check I'm not missing any.

Bob


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

#3 2013-07-23 23:33:50

debjit625
Full Member

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Re: Trigonometric equation problem...

Hi bob

When I  solve the equation

as
my answer is


And when I solve the equation
as
my answer is
or
.

Now which one is correct ,are both correct?

Now putting the different values for "n" we can get the value for theta and put it in the equation and check,but I did just a couple and I know if I can graph it it will show but which application to use for this kind of job I dont know.

Thanks

Last edited by debjit625 (2013-07-23 23:35:10)


Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

#4 2013-07-24 00:53:13

bob bundy
Moderator

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Re: Trigonometric equation problem...

hi

Not



The divide by 6 must be inside the bracket or you will be dividing an integer n by 6 and not necessarily getting a multiple of pi



is good.  For the other I had



but your answer of



comes to the same as 1/3 plus 2/3 makes an integer ... just a different value of n is required to make my answers into yours.

This is how I did it:



Basic solutions are



so



general solutions:



so general solution for theta



I then just tidied up the algebra a bit.

Bob


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

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