Find the amplitude, if it exists, and the period of: y=cos3x.
|a|=|1|
amplitude = 1
period = 360/b
period = 360/3
period = 120 degrees
yes
To find the amplitude and period of the function y = cos(3x), we can use the general form of the cosine function:
y = A * cos(Bx)
where A represents the amplitude and B represents the coefficient of x, which affects the frequency and period of the function.
In this case, the coefficient of x is 3, so B = 3.
The amplitude of the cosine function is defined as the absolute value of the coefficient A. Since A is not explicitly given in the equation, we know that it is equal to 1 by default.
Therefore, the amplitude of y = cos(3x) is 1.
Next, to determine the period of the function, we can use the formula:
Period (in degrees) = 360 / B
where B is the coefficient of x.
In this case, B = 3, so the period is calculated as follows:
Period = 360 / 3
Period = 120 degrees
Hence, the amplitude of the function y = cos(3x) is 1, and the period is 120 degrees.