Evaluate :sin(nπ+(−1)nπ4) where n is an integer,
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If n=1 then sin(pi/2)=1
If n=2 then sin(pi)=0
If n=3 then sin(3pi/2) = sin(pi+pi/2)= -sin(pi/2)= -1
If n=4 then sin(2pi)=0
If n=5 then sin(5pi/2)= sin(2pi+pi/2)= sin(pi/2)= 1.
Hence sin n*(pi/2)
= 1 if n=1,5,9,13...
= -1 if n=3,7,11,15...
= 0 if n is even
If n=2 then sin(pi)=0
If n=3 then sin(3pi/2) = sin(pi+pi/2)= -sin(pi/2)= -1
If n=4 then sin(2pi)=0
If n=5 then sin(5pi/2)= sin(2pi+pi/2)= sin(pi/2)= 1.
Hence sin n*(pi/2)
= 1 if n=1,5,9,13...
= -1 if n=3,7,11,15...
= 0 if n is even
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