rought said:
The graph of two cosine/sine waves shows the relationship between two periodic functions. The x-axis represents time or distance, while the y-axis represents the amplitude of the waves. The intersection points indicate when the two waves have the same amplitude and direction. You can also determine the frequency and phase shift of each wave by analyzing the graph.
A cosine wave is a function that oscillates between a maximum and minimum value with a period of 2π. It starts at its maximum value and then decreases, reaching its minimum value at π before increasing again. On the other hand, a sine wave starts at 0 and increases to its maximum value at π/2 before decreasing. The two waves have the same shape, but they are shifted by π/2.
The amplitude of a cosine/sine wave is the distance from the midline to the peak of the wave. It represents the maximum displacement or height of the wave. In a graph, you can determine the amplitude by finding the distance between the maximum and minimum points on the y-axis.
The frequency of a cosine/sine wave is the number of complete cycles it completes in a given interval. It is measured in hertz (Hz). In a graph, you can calculate the frequency by counting the number of peaks or troughs in one period (2π) and dividing it by the period. The period is the length of one complete cycle.
The phase shift of a cosine/sine wave is the horizontal displacement or shift of the wave from its original position. It is measured in radians (or degrees). In a graph, you can determine the phase shift by finding the horizontal distance between the midline and the starting point of the wave. This distance is equal to the phase shift.