Understanding Trigonometry

Drag the triangle to different sizes and watch the trig functions recalculate in an easy-to-understand way. Why is the Cosine of angle A equal to the Sine of angle B? Can you make a triangle with a Tangent of 1? Why is it easier to calculate Sine and Cosine when the Hypotenuse is length 10 or 100? Each trig line has its own 'hide' button so you can keep it simple to begin with.

The 4 transformations - Translation

Use the mouse to draw some shapes. Then use the translate button to create your translated copy. You can change the translation vector, then create another copy of your images. Don't forget to try the zoom facility.

The 4 transformations - Enlargement

Use the mouse to draw some shapes. Optional guidelines show by default. Amend the scale factor as required. Then use the 'enlarge' button to create your transformation. Scale factors can be less than one or even negative, which creates a new set of guidelines. Use the top right up/down arrows to change the centre of enlargement and watch the guidelines change in step. Don't forget to zoom.

The 4 transformations - Reflection

Use the top right radio buttons to select a line of reflection. If selecting y=0 or x=0 then you can use the axis arrows to move the line of reflection up/down or left/right. Now use the mouse to draw some shapes and press the 'reflect' button to see the transformation. You can now change the line of reflection and reflect again. Don't forget to zoom.

The 4 transformations - Rotation

Use the mouse to draw some shapes. Set the degrees of rotation. The 'clockwise' button toggles to 'anticlockwise' if required. Optionally change the centre of rotation. Then press the 'rotate' button and watch the rotation. Change some settings and rotate again. Be sure to try the zoom facility.

Circle Geometry

Choose the setting from the drop-down combo box. Then drag the blue handles to change the triangles. Each angle can be hidden or shown separately to encourage the setting of challenges.

Graphs - Straight Lines and Curves

Use the drop-down box (top left) to select the required graph type. Then use the blue up/down buttons to set your required equation or just experiment and observe the effects of adjusting each component. By default, each change to the equation replaces the old graph with the latest. To overlay graphs just click on the Keep Previous check-box (bottom right). The Draw on Change check-box (bottom right) causes a new graph to be drawn each time the equation is modified. Click on this check-box to turn off this feature and just use the Draw Graph button when required.

Graphs - Trigonometry

This activity uses similar buttons and check-boxes to graphing tool above. The available functions are:
y= aSin(bx +c),
y= aCos(bx +c)
y= aTan(bx +c), where c will increment/decrement in multiples of 15 degrees.

This activity is ideal for demonstrating the effects of changing each component of the trig functions eg the difference between y= 2Sin(x) and y Sin(2x)

Pythagoras Theorem - Visual and Algebraic Proof

This is essentially a novel way of demonstrating visually Pythagoras' theorem. You may want to show it first without the algebra. Then use the 'restart' button and tick the 'show algebra' box. With this option on there's an extra few frames at the end working out the algebra - don't miss them!