Question

Identify the period of the graphed cosine function.

Answer 1

Explanation:

the (x-axis) interval between two maximums or two minimums of the waves is known as a period.

it is tricky to find this here, when we only look at 2 e.g. maximums next to each other.

they mostly don't have "nice numbers" we can identify directly on the graph (as they go through grid-line crossing points).

but a few maximums have nice numbers as coordinates :

(0, 2)

(2pi, 2)

(-2pi, 2)

...

what do we notice ?

these nice numbers happen at every third maximum.

the distance between 4 maximums (containing 3 periods) is 2pi.

since it is a cosine function, we know, it is a truly regular, periodic function, and every distance between 2 maximums is the same.

therefore, since the distance of 4 maximums (with 3 periods) is 2pi, the distance between 2 maximums (1 period) is then 2pi/3.

Answer 2

`\textsf{Period}=(2\pi)/(3)`

Explanation:

The period of a cosine function is the horizontal distance between two consecutive points where the function repeats its pattern, such as from one peak to the next peak, or one trough to the next trough.

The coordinates of the consecutive peaks or troughs of the graphed cosine function are challenging to determine directly. However, we can see that there is a peak at (0, 2) and another peak at (2π, 2), and that the curve completes three full cycles within this interval. Therefore, we can calculate the period by taking the difference between the x-values of these two points and dividing by the number of cycles (3):

`\textsf{Period}=(2\pi - 0)/(3)=(2\pi)/(3)`

So, the period of the graphed cosine function is 2π/3.