Find the period and amplitude of the sin function.
y= -34sin(3x)
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The general form of a sin function can be written as y = A sin(Bx + C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.
In this case, y = -34sin(3x), so we can see that A = -34 and B = 3.
The amplitude is the absolute value of the coefficient of the sin function, so the amplitude is 34. Since the coefficient is negative, this tells us that the function is reflected over the x-axis.
The period of a sin function is given by the formula T = 2π/B. So, in this case, T = 2π/3.
Therefore, the period is 2π/3 and the amplitude is 34.
To find the period and amplitude of the sine function y = -34sin(3x), we use the general form of the sine function:
y = A*sin(Bx + C) + D
Comparing this form with the given function, we can see that:
Amplitude (A) = -34
The amplitude value represents half the distance between the maximum and minimum values of the function. In this case, the amplitude is 34. Since the function is multiplied by -34, the graph will be inverted and the amplitude will also be negative.
To find the period of the function, we use the formula:
Period (P) = 2π / |B|
In this case, B = 3. Therefore, the period is:
P = 2π / |3| = 2π / 3
Hence, the period of the sine function y = -34sin(3x) is 2π / 3 and the amplitude is -34.
To find the period and amplitude of the sin function y = -34sin(3x), we need to understand the general form of the sine function:
y = A * sin(Bx + C) + D
In this form, A represents the amplitude, B determines the frequency and the period is given by T = 2π/B.
For our given function, y = -34sin(3x), we can see that:
A = -34 (amplitude)
B = 3 (frequency)
So, the amplitude is 34 and the frequency is 3. To find the period, we use the formula:
T = 2π / B
Substituting B = 3, we have:
T = 2π / 3
Therefore, the period of the function y = -34sin(3x) is 2π/3 and the amplitude is 34.