The discussion revolves around graphing the function x(t) = 10cos((pi*t)-(pi/4)), focusing on understanding its amplitude, frequency, and phase shift. Participants are examining the characteristics of the cosine function in relation to transformations applied to it.
Some participants have provided insights into the relationship between angular frequency and the period of the function, while others are exploring the implications of the phase shift on the graph. There is an ongoing examination of the transformations without a clear consensus on the interpretation of the frequency.
There is a mention of homework constraints and the need to accurately represent the transformations in the graphing process. Participants are navigating through the implications of the function's parameters without resolving all uncertainties.
I don't think so. You could write this function as x(t) = 10 cos(pi(t - 1/4)). The graph of x(t) = 10 cos(pi*t) has two transformations: a vertical expansion by a factor of 10 (that's your amplitude), and a compression toward the vertical axis by a factor of pi. This compression means that instead of having t intercepts at +/-pi/2, +/-3pi/2, +/-5pi/2, and so on, x(t) = 10 cos(pi*t) has t intercepts at +/-1/2, +/-3/2, +/-5/2, and so on.jayare81 said:Homework Statement
plot x(t) = 10cos((pi*t)-(pi/4))
Homework Equations
pi/4 is the shift to the right
jayare81 said:10 is the amplitude of the graph
pi is the radian frequency
The Attempt at a Solution
so i got the amplitude and shift to the right by pi/4 part but as for the radian frequency, my plot doesn't seem right. does pi mean that one cos wave occurs in a pi interval? thanks in advance