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I don't understand this formula?! (2n+1)π/2

Adorable98

Like how can I use it? what is 'n' in this case?!

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Reply 1

Andy98

Original post by Adorable98

Like how can I use it? what is 'n' in this case?!

Basically means if you want a root of cosine, you substitute any value of n into the equation

Reply 2

Adorable98

Original post by Andy98

Basically means if you want a root of cosine, you substitute any value of n into the equation

Could you please give me an example? :smile:

Reply 3

Andy98

Original post by Adorable98

Could you please give me an example? :smile:

If you wanted the second root, you'd do

\frac{((2*2)+1)π}{2}=\frac{3π}{2}

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Reply 4

Adorable98

Original post by Andy98

If you wanted the second root, you'd do

\frac{((2*2)+1)π}{2}=\frac{3π}{2}

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I see, thank you.

Reply 5

Andy98

Original post by Adorable98

I see, thank you.

Yeah, should be 5 not 3, my bad :colondollar:

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Reply 6

MagneticNorth

Original post by Andy98

Basically means if you want a root of cosine, you substitute any value of n into the equation

The roots of the cosine curve you drew are the points where it intersects with the X-axis. These turned out to be: -3PI/2, -PI/2, PI/2, 3PI/2
So the pattern of these roots is: (2n+1)PI/2
when n=-2: the root is ((2*-2)+1)PI/2= -3PI/2
when n=-1: the root is ((2*-1)+1)PI/2= -PI/2
when n=0: the root is ((2*0)+1)PI/2= PI/2
when n=1: the root is ((2*1)+1)PI/2= 3PI/2
Since the cosine curve is periodic, it will keep following the same shape forever, and so will keep crossing the X-axis many more times. So it has an infinite number roots (and not just 4), and has to be written in the general form (2n+1)PI/2.
:smile:

Reply 7