Functions
The period of the function f(x) = sin(4x) + cos(3x) is
Select the correct option:
Solution
2π
- Individual Periods:
- Period of sin(4x) is P1=42π=2π.
- Period of cos(3x) is P2=32π.
- Combined Period: The period of the sum is the LCM of the individual periods.
- LCM of Fractions: LCM(2π,32π)=HCF(denominators)LCM(numerators).
- Calculation:
- Numerators: π,2π⟹LCM=2π.
- Denominators: 2,3⟹HCF=1.
- Result: Period =12π=2π.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- functions
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
2π
- Individual Periods:
- Period of sin(4x) is P1=42π=2π.
- Period of cos(3x) is P2=32π.
- Combined Period: The period of the sum is the LCM of the individual periods.
- LCM of Fractions: LCM(2π,32π)=HCF(denominators)LCM(numerators).
- Calculation:
- Numerators: π,2π⟹LCM=2π.
- Denominators: 2,3⟹HCF=1.
- Result: Period =12π=2π.
This medium difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of functions. It appeared in the 2025 exam.
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