Sine / Cosecant
(Horizontal Transformations)

How to Use This Applet

The Slider Area

The sliders change the parameters b and c in the trigonometric functions y = sin[ b( x − c¹ ) ] or y = csc[ b( x − c¹ ) ].

  • Drag a slider to change the value of a parameter.
  • The <LEFT> and <RIGHT> arrow keys can be used to change the selected parameter [light blue].
  • The <UP> and <DOWN> arrow keys can be used to increase or decrease the selected parameter. (Use this feature for fine adjustments.)
  • If the arrow keys don't respond, click the cursor in the applet frame then try again.
  • Drag a parameter scale to "move" it. (ie. Change the range but maintain the scale "length".)
  • Drag towards or away from a parameter thumb to "re-scale" the scale.
  • Select the corresponding parameter button to enter a value for a parameter.

The Graph Area

  • Drag the red location (or the light red vertical line) to move the graph horizontally.
  • Drag a location along the graph (not on the light red vertical line) to cause a dilatation or reflection about the light red vertical line.
  • Click and drag any location in the graph area (not on the graph) to see the coordinates of the cursor as well as the coordinates of locations along the graph.
  • The <SHIFT> key: Click and drag in the graph area to move the entire coordinate system.
  • The <CONTROL>+<SHIFT> key: Click and drag in the graph area towards or away from the:
    • x-axis to change the y-axis scale.
    • y-axis to change the x-axis scale.

Other

  • Use the "RESET" button to restore the applet to the initial state.