Question #6452486Fill in the Blank
Algebra-2
Question
The period of the function is ________.
Answer & Analysis
Analysis
Question Analysis
This question involves calculating the period of a cosine function with a horizontal stretch (modified coefficient B).
This question involves calculating the period of a cosine function with a horizontal stretch (modified coefficient B).
Key Concept Explanation
The base period of the parent cosine function is (it repeats every radians).
For a transformed cosine function , the period is calculated as . The coefficient B compresses (if ) or stretches (if ) the graph horizontally.
The base period of the parent cosine function is (it repeats every radians).
For a transformed cosine function , the period is calculated as . The coefficient B compresses (if ) or stretches (if ) the graph horizontally.
Step-by-step Solution
1. Identify the coefficient B in the given function : Here, .
2. Recall the period formula for : .
3. Substitute into the formula:
1. Identify the coefficient B in the given function : Here, .
2. Recall the period formula for : .
3. Substitute into the formula:
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