# A question about sine and cosineWatch

#1

If sine and cosine are calculated by an infinite series

How is it that we can get a rational result when we find the sine and cosine of some numbers? (like pi, pi/2 etc.)

Cheers
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9 years ago
#2
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9 years ago
#3
For a start and aren't rational numbers It's just one of those wonderful things about maths.

Which is awesome.
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9 years ago
#4
Infinite series can sum to rational numbers?
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9 years ago
#5
Consider the geometric series with first term = 10 and common ratio = 0.5.

The sum to infinity = a/(1-r) = 20.

There, the sum of an infinite series equals a pretty much rational number.
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9 years ago
#6
(Original post by nuodai)
For a start and aren't rational numbers It's just one of those wonderful things about maths.

Which is awesome.
Maybe the OP meant sin(pi), sin(pi/2) etc, lol
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9 years ago
#7
(Original post by musabjilani)
Maybe the OP meant sin(pi), sin(pi/2) etc, lol
I had an inkling that this might be the case... in which case the OP need look no further than a circle of radius 1 and origin (0, 0)... then it becomes more or less self-descriptive.
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#8
(Original post by musabjilani)
Consider the geometric series with first term = 10 and common ratio = 0.5.

The sum to infinity = a/(1-r) = 20.

There, the sum of an infinite series equals a pretty much rational number.
But I don't think the series for sine and cosine have a common ratio...
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#9
(Original post by nuodai)
I had an inkling that this might be the case... in which case the OP need look no further than a circle of radius 1 and origin (0, 0)... then it becomes more or less self-descriptive.
Yes that is what I meant, although I don't see how the way of displaying sine and cosine in a circle relates to calculating them as an infinite series
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9 years ago
#10
(Original post by j09)
Yes that is what I meant, although I don't see how the way of displaying sine and cosine in a circle relates to calculating them as an infinite series
It dosen't - they can be shown to be equivalent though.

(Original post by j09)
But I don't think the series for sine and cosine have a common ratio...
how can you accept that that sums to a rational number nut the series epansion for trig functions does not?
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