SOLUTION: If f(x)= cos x and f(a)= -1/12 find the exact value of f(a) + f(a-2pi) + f(a+4pi)

Question 601506: If f(x)= cos x and f(a)= -1/12 find the exact value of f(a) + f(a-2pi) + f(a+4pi)
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since cos(x+k*2pi) = cos(x) for any integer k, this means that cos(a-2pi) = cos(a) and cos(a+4pi) = cos(a)

This means that

f(a) + f(a-2pi) + f(a+4pi) = f(a) + f(a) + f(a) = 3*f(a) = 3*(-1/12) = -3/12 = -1/4

So f(a) + f(a-2pi) + f(a+4pi) = -1/4
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If f(x)= cos x and f(a)= -1/12
find the exact value of f(a) + f(a-2pi) + f(a+4pi)
------------------------------
Equation:
exact value of f(a) + f(a-2pi) + f(a+4pi)
(-1/12) + (-1/12) + (-1/12)
---
= -3/12
= -1/4
================
Cheers,
Stan H.

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