1. Let's start by stating the problem: We want to understand why frequency equals a certain value or expression in a given context. 2. Frequency generally refers to the number of occurrences of a repeating event per unit time. In physics and mathematics, frequency $f$ is related to the period $T$ (the time for one complete cycle) by the formula: $$f = \frac{1}{T}$$ This means frequency is the reciprocal of the period. 3. Important rule: If you know the period of a wave or oscillation, you can find the frequency by taking the inverse. 4. For example, if the period $T = 0.5$ seconds, then frequency is: $$f = \frac{1}{0.5} = 2$$ This means the event repeats 2 times per second. 5. This relationship holds because frequency counts how many cycles happen in one second, and period measures how long one cycle takes. 6. Therefore, knowing one allows you to calculate the other using the formula above. This explains why frequency equals the reciprocal of the period.