Trigonometry is used in many fields, such as construction, surveying, engineering, navigating and many other areas in research as experimental physics.
Trigonometry involves right-angled triangle extensively and there are ratios between the three sides that are useful in many ways. In order to refer to these ratios, the sides are named in relation to the angle being studied:
- the hypotenuse is the longest side, and is always opposite the right angle
- the side opposite to the studied angle marked '' (theta) is the opposite
- the adjacent side is next to the angle marked ''
The trigonometric ratios are:
You may have seen these ratios in your scientific calculators. To remember these ratios easily, use the abbreviations: SOH CAH TOA.
SOH = Sine Opposite Hypotenuse
CAH = Cosine Adjacent Hypotenuse
TOA = Tangent Opposite Adjacent
As well as the basic ratios, there are invese trigonometric ratios:
It is also useful to understand the complementary angles in a right-angled triangle:
1. Find the exact values for cos x, tan x and cosec x.
2. If find .
Think: Why does tan 90° result in ?