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If someone could explain the thought process behind 1F5 from http://ocw.mit.edu/courses/mathematics/1801scsinglevariablecalculusfall2010/partbimplicitdifferentiationandinversefunctions/problemset2/MIT18_01SC_pset1prb.pdf that would be really helpful. Where does the 1^k part from this formula sin(π/2+ kπ)=(−1)^k come from?
(part of the solution @ http://ocw.mit.edu/courses/mathematics/1801scsinglevariablecalculusfall2010/partbimplicitdifferentiationandinversefunctions/problemset2/MIT18_01SC_pset1sol.pdf)
 one year ago
 one year ago
If someone could explain the thought process behind 1F5 from http://ocw.mit.edu/courses/mathematics/1801scsinglevariablecalculusfall2010/partbimplicitdifferentiationandinversefunctions/problemset2/MIT18_01SC_pset1prb.pdf that would be really helpful. Where does the 1^k part from this formula sin(π/2+ kπ)=(−1)^k come from? (part of the solution @ http://ocw.mit.edu/courses/mathematics/1801scsinglevariablecalculusfall2010/partbimplicitdifferentiationandinversefunctions/problemset2/MIT18_01SC_pset1sol.pdf)
 one year ago
 one year ago

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k even, i.e. k=2n for some integer n, then :\[\sin(\pi/2+k \pi)= \sin(\pi/2 + 2n \pi )= 1\]k odd, i.e. k=2n1 for some integer n:\[\sin(\pi/2+k \pi)= \sin(\pi/2 + (2n1) \pi )= 1\] (Remember this from trig? You can see this on a graph of y=sin(theta)) We find the ycoordinates of the points by substituting the xcoordinates into sin(x)+sin(y)=1/2, and using the values calculated above. It turns out only some of the xvalues will give real answers for y, so only these xcoordinates are kept. We are then left with the xcoordinates and ycoordinates that work  the points we wanted.
 one year ago
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