Question

How do you find the period of `y= -4 cos 2x`?

Answer 1

`pi`

Explanation:

Let us look at a more general problem: `f(x) = A cos(nx)`. In this case, we have `f(x + 2pi/n) = A cos(n(x + 2pi/n)) = A cos(nx + 2pi) = A cos(nx)`. Try this also for `sin`; it is exactly the same.

Thus we see that the period of such a general function is `(2pi)/n`.

Therefore for `f(x) = -4 cos(2x)`, the period is `(2pi)/n = (cancel2 pi)/cancel2 = pi`.