Question

How are periodic phenomena relatively easy to model using trig functions? What makes them difficult to model this way?

Answer 1

Answer:

Periodic phenomena means that the phenomena has a (almost) constant time period or space period.

As you know, the trigonometric functions cos(x) and sin(x) also have a constant period of 2*pi, so these functions are really useful to model periodic phenomena.

Now, the problem may be that the trigonometric functions may be useful to describe the "periodic" part, but not to describe the actual phenomena.

An example of this can be a square alternating current.

While it has a constant period like a trigonometric function, the trigonometric functions can not really model the "square" part of this current (you know that the sinusoidal functions actually are curves and continuous)

Here comes something called the Fourier Series, that are series of the form:

F(x) = a₀ + ∑(aₙ*cos(nx) + bₙ*sin(nx))

That can be used to model almost any periodic phenomena, but the actual Fourier Series may be hard to construct.