time in Sine Wave equation

Question

According to Wikipedia,

The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation.

The formula for the Sine wave is,

A = Amplitude of the Wave ω = the angular frequency, specifies how many oscillations occur in a unit time interval, in radians per second φ, the phase, t = ?

Here ω, is the angular frequency i.e ,

It defines how many cycles of the oscillations are there.

Now let see the frequency,

Frequency is the number of occurrences of a repeating event per unit time

For example, if 100 events occur within 15 seconds the frequency is:

Events = 100;
Time = 15;
FREQ = Events/Time;

Which means there is total 100 cycles of wave in 15 seconds , am i correct ?

Events = 71;
Time = 15;
FREQ = Events/Time;
W = 2*PI*FREQ;   % 2*PI for circular path
A = 2 ;

Now what is the use of small 't' ? in the Sine wave equation , what time is it ?

Answer 1

In the context that you described, $t$ is a variable indicating time. That is, the wave will take on a value of $y(t)$ at the time instant $t$. If this is measured in seconds, then $\omega$ specifies the number of radians that the wave passes through in one second. And, as you noted, if the wave has a frequency of $\frac{100}{15}\ \text{Hz}$, then it will pass through 100 periods in 15 seconds.