Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.
Six Trigonometric Functions
1. Sine Function2. Cos Function3. Tan Function4. Secant Function5. Cosecant Function6. Cotangent Function
1. Sine Function
Sine function of an angle is the ratio between the opposite side length to that of the hypotenuse.
Sin a =Opposite/Hypotenuse = CB/CA
2. Cos Function
Cos of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.
Cos a = Adjacent/Hypotenuse = AB/CA
3. Tan Function
The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio.
Tan a = Opposite/Adjacent = CB/BA
Also, in terms of sine and cos, tan can be represented as:
Tan a = sin a/cos a
4. Secant Function
The Secant function The secant function is a periodic function in trigonometry and it can be defined as the ratio of the length of the hypotenuse to that of the length of the base in a right-angled triangle. It is the reciprocal of cosine function and hence, is also written as sec x = 1 / cos x.
5. Cosecant Function
The cosecant function is the reciprocal of the trigonometric function sine. It is one of the main six trigonometric functions and is abbreviated as csc x or cosec x, where x is the angle.
Cosec a = 1/(sin a) = Hypotenuse/Opposite = CA/CB
6. Cotangent Function
The cotangent of an angle in a right‐angle triangle is the ratio of the length of the adjacent leg to the length to the opposite leg.
cot a = 1/(tan a) = Adjacent/Opposite = BA/CB