If the period of a trigonometric function is $T$, how many complete cycles of the function occur in a horizontal length of $L$?

• A. $L-T$
• B. $L+T$
• C. $\frac{L}{T}$
• D. $\frac{T}{L}$

Answer: (C)

Verified step by step guidance

1. Recall that the period \(T\) of a trigonometric function is the length of one complete cycle along the horizontal axis.
2. To find how many complete cycles fit into a horizontal length \(L\), you need to determine how many segments of length \(T\) fit into \(L\).
3. This is done by dividing the total length \(L\) by the period \(T\), which gives the number of complete cycles as \(\frac{L}{T}\).
4. Note that expressions like \(L - T\) or \(L + T\) do not represent the number of cycles; they are just arithmetic operations on lengths and do not correspond to counting cycles.
5. Therefore, the correct formula for the number of complete cycles in length \(L\) is \(\frac{L}{T}\).