1.

Evaluate :sin(nπ+(−1)nπ4) where n is an integer,

Answer»

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


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