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in this instance i was working with

**y=cos2x**, i knew what the graph looked like even before i put pen to paper but i wanted to know exactly where the zeros were, i took an educated guess that each side would have 4 zeros(4 negative 4 positive)

so i found my first zero using trial and error which was 45

THEN it happened i sort of found this pattern

the equation i sort of made up was

cos(2 * what number would =0)

the first number i got was 45, then either i got lucky and discovered this pattern or i remember looking at one of the graphs noticing the zeros were always the same distance apart from each other(They were increasing by the same amount each time)

so i did 45+45= not a zero

but when i did

45+45+45 = Zero (135)

45+45+45+45+45=zero(225)

but 45+45+45+45= not a zero

so it would skip a 45 and the next 45 would be a zero

in other words 45(1) = zero 45(2)=not a zero 45(3)=zero 45(4)=not a zero 45(5)=zero and it would go on and on

my question is what have i stumbled upon here? Is this a special kind of mathematics? They all seem to be odd numbers for zeros.

**This will REALLY come in handy for future problems of similar types, i will no longer find zeros using the exhausting method of trial and error, just use patterns like this to find the zeros and save a lot of time and energy**