Trigonometry

The word trigonometry comes from two Greek words trigon- meaning triangle and metron meaning to measure. Trigonometry is about measuring triangles.

There is a word sine used in trigonometry. This modern word has come to us from a word that originally meant chord or bowstring.

Here is a chord

Here is a chord with a radius joined at each end of the chord

Here is the chord with a third radius added that bisects (cuts in two equal parts) the angle between the first two radii. Two right-angled triangles have been created.

The diagram looks like a bowstring pulled back with an arrow ready to fire. This is where the word sine comes from.

Let’s look at the top right-angled triangle

If we consider the angle labelled θ then the opposite side is labelled O and the hypotenuse is labelled H.

Sine θ = O ÷ H

This might be a little confusing. It is saying something like, bowstring of θ = O ÷ H. The word bowstring or sine isn’t important. It is just saying that if you do sine to θ then you get a value of O ÷ H

Sine θ = O ÷ H

In our example where θ = 53.1, sine θ = 0.8

Every time there is an angle in a right angled triangle of 53.1 then the length of the side opposite it divided by the length of the hypotenuse is 0.8.

This sentence is written in mathematical language as

sine 53.1 = 0.8