To help pupils overcome difficulty in learning trigonometry, try starting with a practical investigation. Give pupils a worksheet with three similar right-angled triangles.
Ask pupils to measure each side of each triangle. From this, they are able to work out the ratios: adjacent: hypotenuse; opposite: hypotenuse and opposite: adjacent.
Taking experimental error into account, pupils should get each of the three ratios correct to two decimal places.
Ask them to explain what they would expect to find for three other similar triangles, having a different angle.
Explain that each ratio has a special name - cosine, sine and tangent, with each ratio for any right-angled triangle having the same value.
This method allows pupils to go on with confidence using trigonometry in current and future lessons.
A useful web resource can be found at www.mathsci.appstate.edu~sjgclass3010finaljane3.pdf
Graham Green is a private tutor in Chesham, Buckinghamshire.