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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bob bundy
2013-07-24 00:53:13

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

debjit625
2013-07-23 23:33:50

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

bob bundy
2013-07-23 22:11:39

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

debjit625
2013-07-23 21:20:43

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

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