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RISC World

Locus

Another exclusive Foundation RISCWorld application

Exercise 10. Calculus


This exercise is only relevant if you are engaged in post 16 mathematics.

There are three Calculus tools available for analysis of cartesian functions.

  • A tangent drawing tool
  • An option to draw the derived function automatically
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  1. Set Radian mode and set the domain to -2pi to 2pi. (Remember that the constant p contains the value of pi, so typing -2p and 2p will do the trick.)
  2. Draw the graph of y=sinx
  3. Now click on the coordinates icon which is on the top row of the main pane and contains a picture containing '(x,y)'. This will open the coordinates window. If you click on the 'toggle size' icon this will also give you information on the polar coordinates of points on the graph and the gradient of the curve at particular points.
  4. Click on the 'Tangent' icon which is to the right of the coordinate icon.
  5. Clicking the mouse in the main window will draw the tangent to the curve at the x-coordinate where you clicked.
  6. You can also hold the mouse button down and drag the tangent along the curve.



This facility is useful for examining how the tangent changes along the length of a curve enabling the gradient function to be sketched.

Note that the coordinates window does not need to be open for the tangent facility to operate.

The second and third tools are much simpler to use. Select the two buttons on the right of the top row showing pictures of dy/dx and an integral sign. Now draw the draw of y=sinx and observe what happens. The original graph is drawn and then the derivative and integral functions are superimposed onto it.

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