Given a circle with radius of 2, which is the degree measure of an arc whose length is 1/2 ?
1 answer:
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a. Factorize the denominator:
Then we're looking for such that
If , then
; if
, then
. So we have
as required.
b. Same setup as in (a):
We want to find such that
Quick aside: for the second term, since the denominator has degree 2, we should be looking for another constant such that the numerator of the second term is
. We always want the polynomial in the numerator to have degree 1 less than the degree of the denominator. But we would end up determining
anyway.
If , then
; if
, then
. Expanding everything on the right then gives
which tells us and
; in both cases, we get
. Then
as required.