Provinf bounded variation

I wish to prove that a function is of bounded variation.
The function i'll regard is f(x) = cos(kx) and i have the
following suggestion.

f in BV([a,b]) if it can be written as a sum of two
functions; one non-decreasing and one non-increasing.

Here i get unsecure because even if i could piece-up
the cosine in monotonous segments, i'd like to use the
following set-up.

On the segments where cosine increases:
+: cos(kx) -: 0
while where cosine decreases:
+: -cos(kx) -: 2cos(kx)

Is it right to regard the problem this way?
Is there a more straightforward approach?
(Only yes or no, please. It's sort of a homework.)

--
Vänligen
Konrad
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Sleep - thing used by ineffective people
as a substitute for coffee

Ambition - a poor excuse for not having
enough sence to be lazy
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