Problem 91 - Algebra and Trigonometry

Question

If you are given the equation of a sine function, how do you determine the period?

Step-by-Step Solution

Answer

To determine the period of a sine function, identify the coefficient of the variable inside the sine function and divide \(2\pi\) by the absolute value of this coefficient. The result is the period of the function.

Step 1: Identifying the Sine Function

Recognize the given function as a sine function. A sine function will usually be in the form \(y = a \sin(bx)\) where a and b are constants.

Step 2: Interpretation of Components

Recognize the role of each component in the given equation. Here, \(b\) is the coefficient that determines the period of the sine function. \(a\), on the other hand, determines the amplitude of the function, but it is not relevant to finding the period.

Step 3: Calculation of the Period

Compute the period of the function. The period of a standard sine function is \(2\pi\). However, the presence of the coefficient \(b\) modifies this period. The period \(P\) of a function in the form \(y = a \sin(bx)\) is given by the formula \(P= \frac{2\pi}{|b|}\).