Transformations of the Sine and Cosine Function
How to Use this Applet
The Slider Area
The sliders change the parameters a, b, h and k in the trigonometric functions y = a sin[ b( x − h¹ ) ] + d and y = a cos[ b( x − h¹ ) ] + d.
- Choose the sine or cosine function by selecting the appropriate button.
- 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. (I.e., 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 to translate the graph
- Drag the light red horizontal line to translate the graph vertically (change k).
- Drag the light red vertical line to translate the graph horizontally (change h).
- Vertically drag a location along the trigonometric graph (not on the light red lines) to cause a scaling about the horizontal light red line (change a).
- Horizontally drag a location along the trigonometric graph (not on the light red lines) to cause a scaling about the vertical light red line (change b).
- Click and drag any location in the graph area (not on the sine 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.
- Use the "RESET" button to restore the applet to the initial state.