DBE April 2019 GR12 TRIG.indd 5 4/18/2019 12:35:40 AM
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Introduction to Trigonometry: Solving Practical Problems, Summaries of Mathematics
This document covers maths trigonometry and Pythagoras theorem
Typology: Summaries
2021/2022
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Trigonometry was developed in ancient civilisations to solve practical problems, such as those encountered in building construction and when navigating by the stars. We will show that trigonometry can also be used to solve some other practical problems. We use trigonometric functions to solve problems in two and three dimensions that involve right-angled triangles and non-right-angled triangles.
5.1 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 : AB^2 BC^2 AC^2
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.
Example: Trigonometric ratios Use the sketch below:
- Write down the trigonometric ratios of angle B and angle C.
- Solve for BD and AB.