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Which of the following function has period 2?
- a)cos [(π/3)x]
- b)cos [(π/2)x]
- c)cos (2π x)
- d)cos (π x)
Correct answer is option 'D'. Can you explain this answer?
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Which of the following function has period 2?a)cos [(π/3)x]b)cos [(π/...
Key Idea: Use period of cos kθ is 2π/k
∴ Period of cos (πx) is 2π/π = 2
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Which of the following function has period 2?a)cos [(π/3)x]b)cos [(π/...
Periodic Functions:
A periodic function is a function that repeats its values after a certain interval. The smallest positive interval after which the function repeats is called the period of the function.
Explanation:
In order to determine the period of each function, we need to analyze the given options one by one.
a) cos [(π/3)x]:
The coefficient of x in the argument of cos is π/3. To find the period, we need to calculate 2π divided by the coefficient of x.
Period = 2π / (π/3) = 6
Therefore, the period of cos [(π/3)x] is 6, not 2.
b) cos [(π/2)x]:
The coefficient of x in the argument of cos is π/2. To find the period, we need to calculate 2π divided by the coefficient of x.
Period = 2π / (π/2) = 4
Therefore, the period of cos [(π/2)x] is 4, not 2.
c) cos (2π x):
The coefficient of x in the argument of cos is 2π. To find the period, we need to calculate 2π divided by the coefficient of x.
Period = 2π / (2π) = 1
Therefore, the period of cos (2π x) is 1, not 2.
d) cos (π x):
The coefficient of x in the argument of cos is π. To find the period, we need to calculate 2π divided by the coefficient of x.
Period = 2π / π = 2
Therefore, the period of cos (π x) is 2.
Conclusion:
Among the given options, the function cos (π x) has a period of 2. This means that the function repeats its values every 2 units along the x-axis.
A periodic function is a function that repeats its values after a certain interval. The smallest positive interval after which the function repeats is called the period of the function.
Explanation:
In order to determine the period of each function, we need to analyze the given options one by one.
a) cos [(π/3)x]:
The coefficient of x in the argument of cos is π/3. To find the period, we need to calculate 2π divided by the coefficient of x.
Period = 2π / (π/3) = 6
Therefore, the period of cos [(π/3)x] is 6, not 2.
b) cos [(π/2)x]:
The coefficient of x in the argument of cos is π/2. To find the period, we need to calculate 2π divided by the coefficient of x.
Period = 2π / (π/2) = 4
Therefore, the period of cos [(π/2)x] is 4, not 2.
c) cos (2π x):
The coefficient of x in the argument of cos is 2π. To find the period, we need to calculate 2π divided by the coefficient of x.
Period = 2π / (2π) = 1
Therefore, the period of cos (2π x) is 1, not 2.
d) cos (π x):
The coefficient of x in the argument of cos is π. To find the period, we need to calculate 2π divided by the coefficient of x.
Period = 2π / π = 2
Therefore, the period of cos (π x) is 2.
Conclusion:
Among the given options, the function cos (π x) has a period of 2. This means that the function repeats its values every 2 units along the x-axis.
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Which of the following function has period 2?a)cos [(π/3)x]b)cos [(π/2)x]c)cos (2π x)d)cos (π x)Correct answer is option 'D'. Can you explain this answer?
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