Instantaneous Values

An ac sine wave has a characteristic shape, as shown in following figure. This is the way the graph of the function y = sin x looks on an (x,y) coordinate plane. (The abbreviation sin stands for sine in trigonometry.) Suppose that the peak voltage is 1 V, as shown. Further imagine that the period is 1 s, so the frequency is 1 Hz. Let the wave begin at time t = 0. Then each cycle begins every time the value of t is a whole number. At every such instant, the voltage is zero and positive-going.

A sine wave with a period of 1 second. It thus has a frequency of 1 Hz.

If you freeze time at, say, t = 446.00, the voltage is zero. Looking at the diagram, you can see that the voltage will also be zero every so-many-and-a-half seconds, so it will be zero at t = 446.5. But instead of getting more positive at these instants, the voltage will be negative-going. If you freeze time at so-many-and-a-quarter seconds, say t = 446.25, the voltage will be +1 V. The wave will be exactly at its positive peak. If you stop time at so-many-and-three-quarter seconds, say t = 446.75, the voltage will be exactly at its negative peak, −1 V. At intermediate times, say, somany-and-three-tenths seconds, the voltage will have intermediate values.