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

1. Like how can I use it? what is 'n' in this case?!
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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
3. (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?
Could you please give me an example?
If you wanted the second root, you'd do

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5. (Original post by Andy98)
If you wanted the second root, you'd do

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I see, thank you.
I see, thank you.
Yeah, should be 5 not 3, my bad

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7. (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.
8. Note that n is a whole number, though that's probably obvious
...
All that it's saying is that the roots of which are the solutions to the equation occur at odd multiples of . So they could occur at 1 multiple of or 3 multiples or 5 multiples, or -3 multiples or -101 multiples etc... as just odd multiples of .

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