Trigonometric Functions
Share This Maths Concept
The ratio between any two sides of a right angle triangle is defined a trigonometric function and ratio between different sides of same right angle triangle can be taken in 3! ways i.e 6 ways. We name to each ratio for our convenience because expressing ratios of two sides and also developing trigonometric fundamentals with same ratios confuse us and also create so many problems in studying this mathematical concept Trigonometry. Hence, we name to each ratio. As per our definition we understood that we take ratio between two sides. Therefore we also call them, trigonometric ratios. In other words we can call those six ratios as trigonometric ratios and also trigonometric functions. The lists of ratios’ names are given below.
- Sine
- Cosine
- Tangent
- Co-Tangent
- Secant
- Cosecant
However, these six trigonometric functions are written in short form which means Sine, Cosine, Tangent, Co-Tangent, Secant and Cosecant are abbreviated as Sin, Cos, Tan, Cot, Sec and Cosec respectively but without integrating angle to these functions become meaningless. Hence we are going to explain it with a right angle triangle.
Consider a right angle triangle whose angle is θ and sides of the respective right angle triangle is Opposite Side, Adjacent Side (Some people call it as base) and Hypotenuse. As we already know these sides’ ratios can be taken in six ways and these ratios are known Trigonometric Functions or Trigonometric Ratios. Now we express Sine, Cosine, Tangent, Cotangent, Secant and Cosecant functions as Sin θ, Cos θ, Tan θ, Cot θ, Sec θ and Cosec θ because trigonometric ratios are dependents on angle.
It is time to define each trigonometric ratio by considering possible ratios of any two sides of a right angle triangle.
Sine
The ratio between length of the opposite side of a right angle triangle and its length of hypotenuse is defined Trigonometric Function Sine and it can be expressed in mathematical form as stated below.
| Sin θ | = | Length of the Hypotenuse |
Share This Maths Tutorial
Related Concepts
- Relationship between Trigonometric Functions
- Trigonometric Equations & Solutions
- Inverse Trigonometry
- Properties of Triangles
- Heights and Distances
- Hyperbolic Functions
- Complex Numbers
Cosine
The ratio between length of the adjacent side of a right angle triangle and its length of hypotenuse is defined Trigonometric Function Cosine and it can be expressed in mathematical form as stated below.
| Cos θ | = | Length of the Hypotenuse |
Tangent
The ratio between length of the opposite side of a right angle triangle and its length of adjacent side is defined Trigonometric Function Tangent and it can be expressed in mathematical form as stated below.
| Tan θ | = | Length of the Adjacent Side |
Cotangent
The ratio between length of the adjacent side of a right angle triangle and its length of opposite side is defined Trigonometric Function Cotangent and it can be expressed in mathematical form as stated below.
| Cot θ | = | Length of the Opposite Side |
Secant
The ratio between length of the hypotenuse of a right angle triangle and its length of adjacent side is defined Trigonometric Function Secant and it can be expressed in mathematical form as stated below.
| Sec θ | = | Length of the Adjacent Side |
Cosecant
The ratio between length of the hypotenuse of a right angle triangle and its length of opposite side is defined Trigonometric Function Sine and it can be expressed in mathematical form as stated below.
| Cosec θ | = | Length of the Opposite Side |