Math Problem Statement

Consider the sinusoidal function seen in the graph below. What is the frequency of this function? Write your answer to the nearest whole number.

Solution

To determine the frequency of a sinusoidal function from a graph, you'll need to observe the number of complete cycles the wave completes over a certain interval—usually one second if time is on the x-axis. The frequency is the reciprocal of the period, which is the length of one complete cycle.

Here is a step-by-step guide on how you could find the frequency if looking at a graph:

  1. Identify the Period: Look at the graph and determine the distance (along the x-axis) between two successive points where the wave begins repeating itself. These points could be consecutive peaks, troughs, or any identical points following the wave's pattern. Measure this distance; that is the period of the function.

  2. Calculate the Frequency: The frequency (f) is the reciprocal of the period (T). If the period is measured in seconds, frequency will be in hertz (Hz), given by the formula: f=1Tf = \frac{1}{T}

  3. Round to the Nearest Whole Number: Once you compute the frequency, round the result to the nearest whole number.

Without seeing the actual graph, I cannot provide a specific numerical answer, but these steps will allow you to find the frequency using the graph.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Sinusoidal Functions
Frequency and Period

Formulas

Frequency (f) = 1 / Period (T)

Theorems

Reciprocal Relationship Between Frequency and Period

Suitable Grade Level

Grades 9-12