Trigonometry Grade 12

Trigonometric ratios, identities and reduction
Definitions: The trigonometric ratios are for right-angled triangles. These ratios all involve one
angle (other than the right angle) and the length of two sides. The ratios can be used to find the
length of an unknown side or an angle if the other two quantities are known.
The Pythagoras theorem states that for any right-angled triangle, the square on the
hypotenuse is equal to the sum of the square of the other two sides.
The converse of this theorem states that if the square on the longest side of the triangle is equal
to the sum of the square of the other two sides, then the triangle is a right-angled triangle.
Pythagoras: 2 2 2 AB BC AC
Hints for solving two-dimensional problems using trigonometry and the Pythagoras
theorem.
• If you are not given a diagram, draw one yourself.
• Mark all right angles on the diagram and fill in the figures for any other angles and lengths
that are known.
• Mark the angles or sides that you have to find.
• Identify the right-angled triangles that you can use to find the missing angles or sides.
9 Decide what mathematical method you will use: Pythagoras, sin, cos or tan.
• Later in the problem, if you have to use a value that you have calculated, use the most
accurate value and only round off at the end.