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debjit625

Member

Registered: 2012-07-23

Posts: 101

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

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

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

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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

debjit625

Member

Registered: 2012-07-23

Posts: 101

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 01:35:10)

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

---

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