How do you know what the period of this function is: y=2cos3(x+45')? Explain.
y = 2cos(3x+135)
cos(kx) has period 2pi/k, so y has period 2pi/3.
The 135 is just a phase shift, and does not affect the period.
Ok thanks a lot for your help steve :D
To determine the period of the function y = 2cos3(x+45'), we need to understand the concept of the period of a cosine function.
The general form of the cosine function is y = A*cos(Bx + C), where A represents the amplitude, B represents the frequency, and C represents the phase shift.
The period of a cosine function is the distance it takes for the cosine function to complete one full cycle. In other words, it is the length of the interval that is repeated to create the graph of the function.
For a basic cosine function, y = cos(x), the period is 2π. However, when we introduce a coefficient in front of the x, as in y = cos(Bx), the period of the function changes.
In this case, we have y = 2cos3(x+45'). The coefficient in front of x is 3, which means that the graph will oscillate three times as fast as the basic cosine function.
To calculate the period of this function, we can use the formula:
Period = 2π/B
In our case, B = 3, so the period is given by:
Period = 2π/3
Hence, the period of the function y = 2cos3(x+45') is 2π/3.
To summarize, we determined the period of the function by applying the formula for the period of a cosine function, which is 2π divided by the frequency of the function. In this case, the frequency is represented by the coefficient in front of x, which is 3.