Graphing Sine and Cosine Functions
Recall that the sine and cosine functions relate real number values to the
Plotting the points from the table and continuing along the
Graph of the sine function
Graph of points with
Notice how the sine values are positive between
Plotting values of the sine function
The points on the curve
Now let’s take a similar look at the cosine function,
As with the sine function, we can plots points to create a graph of the cosine function.
Graph of the cosine function
The points on the curve
Because we can evaluate the sine and cosine of any real number, both of
these functions are defined for all real numbers. By thinking of the
sine and cosine values as coordinates of points on a unit circle, it
becomes clear that the range of both functions must be the interval
Identifying Periodic Functions
In the graphs for both sine and cosine functions, the shape of the graph repeats after
for all values of
Periods of the sine and cosine functions
The sine and cosine functions are periodic, meaning that
a specific horizontal shift,
Even and Odd Functions
Looking again at the sine and cosine functions on a domain centered at the
Odd symmetry of the sine function
The sine function is odd, meaning it is symmetric about the origin.
The graph of the cosine function shows that it is symmetric about the y-axis. This indicates that it is an even function. For even functions, any two points with opposite
Even symmetry of the cosine function
The cosine function is even, meaning it is symmetric about the