We can determine the amplitude of cosine functions by comparing the function to its general form. The general form of a cosine function is: In general form, the coefficient A is the amplitude of the cosine. If there is no number in front of the cosine function, we know that the amplitude is 1.

We should have a cosine function to talk about. I will use A⋅ cosθ. A plot of the basic cosine has a max value of 1 and a minimum of -1. Remember that a plot of the cosine is a wave. The magnitude of that wave is 1. So for any value of θ, the amplitude of the cosine function A ⋅ cosθ = |A|.

The amplitude of y = a sin ( x ) and y = a cos ( x ) represents half the distance between the maximum and minimum values of the function. Amplitude = | a | Let b be a real number. The period of y = a sin ( b x ) and y = a cos ( b x ) is given by Period = 2 π | b |

Solution : i) By observing the pattern, it is the graph of cosine function. Every cosine functions will be in the form y = A cos Bx Midline is x = 0, maximum = 4 and minimum = -4 Amplitude = (max - min)/2 = (4 - (-4))/2 = (4 + 4)/2 = 8/2 = 4 ii) Horizontal length of one cycle = 2π Period = 2π/|B|