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Reflect Again

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

Rots and Refs

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

Sine Problem

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

Squaring the Rectangle

Age 14 to 18 Challenge Level:
Here is a rectangle drawn on a set of axes. If the top right corner of the rectangle has coordinates (a, b), how could you calculate the coordinates of the other dots?