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the sine is zero the cosine is one the
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the sine is zero the cosine is one the
sine is zero so minus 0 is also zero the
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sine is zero so minus 0 is also zero the
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sine is zero so minus 0 is also zero the
cosine is one but now there's a minus
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cosine is one but now there's a minus
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cosine is one but now there's a minus
one and now I'm back where I started and
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one and now I'm back where I started and
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one and now I'm back where I started and
so the pattern will repeat
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so the pattern will repeat
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so the pattern will repeat
ok so the values of the derivatives are
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ok so the values of the derivatives are
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ok so the values of the derivatives are
all zeros and plus and minus ones and
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all zeros and plus and minus ones and
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all zeros and plus and minus ones and
they go through that pattern
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they go through that pattern
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they go through that pattern
fourfold periodicity over and over again
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fourfold periodicity over and over again
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fourfold periodicity over and over again
and so we can write out
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and so we can write out
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and so we can write out
what the sine of X is using Taylor's
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what the sine of X is using Taylor's
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what the sine of X is using Taylor's
formula using this formula so I put in
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formula using this formula so I put in
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formula using this formula so I put in
the value it's zero which is zero then I
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the value it's zero which is zero then I
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