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For how many values of n with 0<=n<=100 is the graph of f(x) = sin(x + n) identical to the graph of g(x) = cos(x)?

I think that I should use the relationship that cos(x)=sin(90-x) but I'm not sure how.

2 answers

we want

sin(x+n) = cos(x)
sin(x)cos(n) + cos(x)sin(n) = cos(x)

we need cos(n)=0 and sin(n)=1
This is true only for n = 2k*pi + pi/2

for k=0,1,2,3...
that is pi/2, 5pi/2, 9pi/2, ...

100 * 2/pi = 63.6, so the last entry in the list is 61pi/2 = 95.8
Does that mean there's 16 values of n?