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How do you find the period and frequency of cosine functions that are squared?

a) Period = 2π, Frequency = 1/(2π)
b) Period = π, Frequency = 1/π
c) Period = π/2, Frequency = 2/π
d) Period = 2π, Frequency = 1/π

User Harry Wood
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Final Answer:

Period = 2π, Frequency = 1/π. Therefore, the correct option is d) Period = 2π, Frequency = 1/π.

Step-by-step explanation:

The period and frequency of a squared cosine function are tied to the properties of the original cosine function. The period of a cosine function squared is influenced by the period of the original cosine function. If the original cosine function, denoted as f(x), has a period T, then the period of f(x)^2 is T/2.

In the context of cosine functions, the standard cosine function has a period of 2π. When you square a cosine function, it compresses the period by a factor of 2. So, if the original cosine function has a period of 2π, the squared cosine function has a period of 2π/2, which simplifies to 2π.

The frequency of a function is the reciprocal of its period. Therefore, if the period of the squared cosine function is 2π, the frequency is 1/(2π).

In the given options, the correct answer is d) Period = 2π, Frequency = 1/π. This aligns with the relationship between the period and frequency of a squared cosine function and the original cosine function. It's essential to understand the fundamental properties of trigonometric functions to analyze and interpret mathematical models and real-world phenomena accurately. Therefore, the correct option is d) Period = 2π, Frequency = 1/π.

User Parse
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