Fundamental Law of Trigonometry

Introduction to Fundamental Law of Trigonometry:-

When we talk about the fundamental law of trigonometry or the very word trigonometry the very first impression that comes in to our minds is right angled triangles. A special branch of geometry dealing with right angled triangles is the basis of trigonometry . When we consider a right angled triangle the first thing that comes to our mind is the hypotenuse which is the longest side of the triangle.The other two sides are the base and the perpendicular ;of course the triangle should have ONE RIGHT ANGLE.

We first determine the ratios of the sides . These are all very special ratios. The ratio between perpendicular and the hypotenuse is called the sine ratio and its inverse is called cosec ratio . The ratio of the base and the hypotenuse is called the cosine or cos ratio and its inverse is called the sec or secant ratio. The ratio between perpendicular and the base is known as the tan ratio and its inverse is known as the cot ratio. Of course all these ratios are in respect to angle theta which is one of the angles in the triangle apart from the right angled triangle.

The Sine Law - Fundamental Law of Trigonometry:

The sine law is such a law in trigonometry that even if we consider a scalene triangle with sides a,b ,c and angles respectively opposite to the sides as A,B,C then a / sinA = b / sinB = c / sinC or even the inverse is true. So if we happen to know any 3 of the data we can find the fourth. So with the help of this wonderful law of trigonometry we can find lots of information regarding the sides and angles of a scalene triangle where there is not necessarily a right angled triangle.

The Cosine Law - Fundamental Law of Trigonometric: -

The cosine law is another wonderful and fundamental law of trigonometry. It states that the square of any one side of a triangle equals the sum of the squares of the other two, less two times their product times the cosine of the angle of the opposite to the first side. That is b^2= a^2+c^2-2ac cos B and a^2= b^2+c^2-2bc cosA and c^2= b^2 + c^2-2ab cos C.