Introduction to Trigonometry
Intro
It is the relationship between the angles and the sides of a right-angle triangle.
Trigonometry Experiment
Intro to Trigonometric Ratios
Here according to the definition of trigonometry, we have to establish a relationship between the angle and the sides of the triangle.
So what we do is find the ratios of the sides of the triangle with respect to the angle .
Here CB is the side opposite to the angle commonly known as the Opposite Side.
And BA is the side adjacent to the angle commonly known as the Adjacent Side.
And CA is the Hypotenuse irrespective of the angle.
So what the ancient mathematicians did is they gave unique names to the ratios of the sides of a right-angle triangle.
1. Sine
2. Cosine
3. Tangent
These are the basic trigonometric ratios that were defined by our mathematicians.
How does it work for all the triangles?
One reason why mathematicians chose a right angle triangle is that value of ratios will remain a constant for a specific angle.
Let's see how it works:
Taking any two right-angle triangles with an angle equal there will be one common right-angle triangle and an angle common.
Using the AA similarity criterion of triangles we can say that all the right-angle triangles with some angle will be similar.
And we also know that the ratio of sides of similar triangles will be the same because similar triangles are just scaled versions of each other.
Therefore, the sine of some angle will remain a constant for any right-angle triangle you pick.
Conclusion
Therefore this is how Ancient mathematicians defined a whole new way of measuring the sides of a triangle using angles.