Trigonometry is all about triangles or to be more precise about the relation between the angles and sides of a rightangled triangle. There are three sides of a triangles named as Hypotenuse, Adjacent, and Opposite. The ratio between these sides based on the angle between them are called Trigonometric Ratios.
As given in the figure in a right angle triangle
There are 6 basic trigonometric relations that form the basics of trigonometry. These 6 trigonometric relations are ratios of all the different possible combinations in a rightangled triangle.
These trigonometric ratios are called
The mathematical symbol θ is used to denote the angle.
A. Sine (sin)
Sine of an angle is defined by the ratio of lengths of sides which is opposite to the angle and the hypotenuse. It is represented as sinθ
B. Cosine (cos)
Cosine of an angle is defined by the ratio of lengths of sides which is adjacent to the angle and the hypotenuse. It is represented as cosθ
C. Tangent (tan)
Tangent of an angle is defined by the ratio of length of sides which is opposite to the angle and the side which is adjacent to the angle. It is represented as tanθ
D. Cosecant (csc)
Cosecent of an angle is defined by the ratio of length of the hypotenuse and the side opposite the angle. It is represented as cscθ
E. Secant(sec)
Secant of an angle is defined by the ratio of length of the hypotenuse and the side and the side adjacent to the angle. It is represented as secθ
F. Cotangent(cot)
Cotangent of an angle is defined by the ratio of length of sides which is adjacent to the angle and the side which is opposite to the angle. It is represented as cotθ.
Trigonometric Ratio  Abbreviation  Formula 
sine  sin  Opposite/Hypotenuse 
cosine  cos  Adjacent/Hypotenuse 
tangent  tan  Opposite/Adjacent 
cosecant  csc  Hypotenuse/Opposite 
secant  sec  Hypotenuse/Adjacent 
cotangent  cot  Adjacent/Opposite 
Solving for a side in right triangles with trigonometry
This is one of the most basic and useful use of trigonometry using the trigonometric ratios mentioned is to find the length of a side of a rightangled triangle But to do, so we must already know the length of the other two sides or an angle and length of one side.
Steps to follow if one side and one angle are known:
Example: In a right angled ΔABC ∠B — 30 length of side A B is 4 find length of BC. given tan30 = 1/√3
Solution:
Steps to follow if two sides are known:
120 videos463 docs105 tests

1. What are trigonometric ratios of a triangle? 
2. How do you calculate the sine of an angle in a triangle? 
3. What is the cosine ratio in a triangle? 
4. How do you find the tangent ratio in a triangle? 
5. Can trigonometric ratios be used in any triangle? 
120 videos463 docs105 tests


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