what is the period of these functions y=1/2 cos 3pi/2
y=2 cos piX/2
To find the period of a function, we need to determine the length of one complete cycle of the function, after which the pattern repeats.
In the first function, y = (1/2)cos(3π/2), we can start by identifying the coefficient in front of the cosine term, which is (1/2). The coefficient affects the amplitude of the function but not its period. So, we can ignore it when finding the period.
The argument of the cosine term, 3π/2, is multiplied by the independent variable, x. To find the period, we need to look at the coefficient in front of the independent variable, which is 3π/2. The period of a cosine function is given by 2π divided by the coefficient of x.
Therefore, for the first function, the period is (2π)/(3π/2). Simplifying this expression, we get:
Period = (2π) * (2/3π) = 4/3
Hence, the period of the first function y = (1/2)cos(3π/2) is 4/3.
Moving on to the second function, y = 2cos(πx/2), we follow the same process. Here, the coefficient in front of the cosine term is 2, which again affects the amplitude but not the period. Thus, we ignore it.
The argument of the cosine function is πx/2. To find the period, we examine the coefficient in front of the independent variable x, which is π/2. Using the same formula as before, we can determine the period:
Period = (2π)/(π/2) = (2π) * (2/π) = 4
Therefore, the period of the second function y = 2cos(πx/2) is 4.