The amount of sunlight in a certain city can be modeled by...

The amount of sunlight in a certain city can be modeled by the function $h=15 \cos \left(\frac{1}{600} d\right)$ where $h$ represents the hours of sunlight, and $d$ is the day of the year. Use the equation to find how many hours of sunlight there are on February $10,$ the $42^{\mathrm{nd}}$ day of the year. State the period of the function.

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Key Concepts

Function Evaluation and Substitution

Evaluating a function by substitution involves replacing the variable with a specific value to calculate the corresponding output. This method is used to determine quantities like the number of hours of sunlight on a particular day when given a complex model.

Trigonometric Modeling of Periodic Phenomena

Using trigonometric functions to model periodic phenomena allows for the representation of natural cycles, such as variations in sunlight or temperature across a year. This approach provides a mathematical framework for analyzing and predicting patterns that repeat over a set period.

Cosine Function

The cosine function is one of the fundamental trigonometric functions that describes smooth, periodic oscillations. It is widely used to model cyclical behavior because its graph repeats in a predictable manner over equal time intervals.

Period of a Trigonometric Function

The period of a trigonometric function is the length of the interval required for the function to complete one full cycle and begin repeating its values. In functions of the form cos(Bx), the period is calculated by dividing 2? by the absolute value of B, illustrating how adjustments in the coefficient affect the cycle's length.

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