Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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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

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

And when I solve the equation
as
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