What is the period of 𝑓 of 𝑥 equals the cos of two 𝑥?
The general period formula is equal
to the regular period of whatever function we’re looking at divided by the absolute
value of 𝐵, where 𝐵 is the number being multiplied to the variable on the inside
of the parentheses. So in this case, 𝐵 must be two
because two is the number being multiplied to the variable on the inside of the
So now we have to know what is the
regular period of the cosine function. And the regular period of the
cosine function is two 𝜋, so we have two 𝜋 divided by the absolute value of
two. And the absolute value of two is
positive two. So two 𝜋 divided by two, the twos
cancel and we get 𝜋.
So when completing these questions,
we have to remember that the period goes from one peak to the next or from any point
to the next matching point, and this can change between functions.