Determine the period, frequency and amplitude of y = 7cos5x - 24sin5x
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To find the period of the given function, we can use the formula:
Period = 2π / |B|
Where B is the coefficient of x in the function. In this case, B = 5. Substituting this into the formula:
Period = 2π / |5|
Period = 2π / 5
The period of the function y = 7cos(5x) - 24sin(5x) is 2π / 5.
To find the frequency, we can use the formula:
Frequency = 1 / Period
Frequency = 1 / (2π / 5)
Frequency = 5 / (2π)
The frequency of the function y = 7cos(5x) - 24sin(5x) is 5 / (2π).
To find the amplitude, we can use the formula:
Amplitude = √(A^2 + B^2)
Where A is the coefficient of the cosine term and B is the coefficient of the sine term. In this case, A = 7 and B = -24. Substituting these values into the formula:
Amplitude = √(7^2 + (-24)^2)
Amplitude = √(49 + 576)
Amplitude = √625
Amplitude = 25
The amplitude of the function y = 7cos(5x) - 24sin(5x) is 25.
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