Exact values for trigonometric ratios

The exact values of cosine, sine and tangent for 30°. 45° and 60° can be found using suitable right angled triangles. See the note.

Explain why the triangles contain the angles 30°, 45° and 60°.

Use Pythagoras' Theorem to show that the triangles are right angled.

Write down the 9 possible ratios and check the values on the calculator.