Student Activity 2 - Graphing y = cscx
I. First, let's set up and examine a table of the coordinates of some of the points that
will satisfy the equation y = cscx.
1. Make a table of values. Label column A "x-coordinates," column B "y-coordinates
of sine," and column C "y-coordinates of cosecant." Set all three columns to round to
4 decimal places.
2. Fill in your x-coordinates in column A by ranging from -2 to 2by increments of
/ 4. Remember, x represents an angular measure - we're using radians as our units.
3. Fill in your y-coordinates in column B by utilizing the equation, y = sinx.
4. Fill in your y-coordinates in column C by utilitzing the relationship between sine
and cosecant.
What do you notice about the values in this column? How do the values in columns B
and C relate? Can you predict what the graph will look like?
II. Graphing in Graphing Calculator.
1. Graph y = sinx from -2 to 2.
2. On the same coordinate plane (but in a different color), graph y = cscx from -2 to
2.
3. Explain what the vertical lines on the graph represent.
4. What is the length of one period of y = cscx?
5. Do cosecant graphs have "amplitude?" Why or why not?
6. How do the graphs of y = sinx and y = cscx relate?
III. Check yourself.
Sketch (by hand!) what the graph of y = cscx will look like, given the following
domain restrictions. Be careful about where the maximums, minimums, and
asymptotes are.
a) 2 to 4
b) -4to 0
c) -3/2to /2