How would you describe the graphs of sine and cosine?
The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.
What does a sine graph represent?
The graphs of functions defined by y = sin x are called sine waves or sinusoidal waves. Notice that the graph repeats itself as it moves along the x-axis. The cycles of this regular repeating are called periods. This graph repeats every 6.28 units or 2 pi radians.
What features are unique to sine and cosine graphs?
The sine and cosine functions have several distinct characteristics:
- They are periodic functions with a period of.
- The domain of each function is and the range is.
- The graph of is symmetric about the origin, because it is an odd function.
- The graph of is symmetric about the axis, because it is an even function.
What do the graphs of sine and cosine have in common with the swinging you see quizlet?
What do the graphs of sine and cosine have in common with the swinging you see? The high and low points repeat in pattern.
Why is sine graph a wave?
The graph of y=sin(x) is like a wave that forever oscillates between -1 and 1, in a shape that repeats itself every 2π units. Specifically, this means that the domain of sin(x) is all real numbers, and the range is [-1,1].
How do you find the equation of a sine graph?
To find the equation of sine waves given the graph:
- Find the amplitude which is half the distance between the maximum and minimum.
- Find the period of the function which is the horizontal distance for the function to repeat.
- Find any phase shift, h.
In what ways can the graphs of sine and cosine be transformed?
Period, Midline, and Amplitude. Changes to the amplitude, period, and midline are called transformations of the basic sine and cosine graphs. Changing the midline shifts the graph vertically. Changing the amplitude stretches or compresses the graph vertically.