Math Problem Statement
What is the period of the function f(x) = cos(8x)?
Solution
To find the period of the function , we use the formula for the period of cosine functions:
Here, is the coefficient of in the argument of the cosine function. In this case, .
Thus, the period of is:
Let me know if you'd like further clarification or have any related questions! Here are some additional questions for exploration:
- What is the amplitude of ?
- How would the period change if where ?
- What is the phase shift of ?
- How does the graph of compare to ?
- What is the frequency of ?
Tip: For trigonometric functions, always identify the amplitude, period, and phase shift to fully describe the function.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Periodic Functions
Formulas
Period of cosine: Period = 2π / |b|, where b is the coefficient of x
Theorems
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Suitable Grade Level
Grades 10-12