Find the period and amplitude of the function: y = -2cos(πx)

Answer 1

The amplitude of a trigonometric function is a nonnegative number which captures how "high" the functions values go. Since cos(k*x) can only go as high or low as +/- 1, this means Acos(k*x) goes up and down between A and -A. Notice that works for both positive and negative A, so we call the amplitude of that function Amplitude = |A|. In our case, the amplitude is Amplitude = |-2| = 2. Now, to find the period for a function like cos(k*x), for any constant k, we need to find the number B, called the period, so that (#) k*B = 2pi. Because the function cos(x) has a period of 2pi (repeats all its values if you start at some x value, and go 2pi to the left or right), we want to find out how often the variable x makes the quantity k*x = 2\pi, since that will cause cos(k*x) to repeat itself. So, solve the equation (#) for B, giving us B = (2*pi)/k. In our case, k = pi so B = (2pi)/(pi) = 2 is the period.