If the length of the hypotenuse is divided by the length of the opposite side, it provides the Cosecant of an angle in a right triangle. One of the trigonometric functions in trigonometry, it is represented as Cosec and occasionally abbreviated as csc.
The Formula for Cosec x is Given as:
Cosec x Formula: Cosec X = Hypotenuse / OppositeSide
What is the Cosecant Formula in Trigonometric Functions?
There are six trigonometric functions in trigonometry among which sin, cos and tan are the primary functions while the sec, cosec and cot are secondary.
Cosecant is the reciprocal of Sin, and thus Cosec x = 1/SinX
What is a Cosecant Function in Maths?
There are different angle functions. Sine, cosine, cosecant, secant, tangent, and cotangent functions are the six elementary functions that are used and incorporated in trigonometry.
Csc, sec and cot are basically the reciprocal functions of sine, cosine and tangent functions respectively. Of the six possible trigonometric functions, the cosecant function is specifically the reciprocal of the sine function.
The definition however does not mention how large the triangle is. Nonetheless, that's where the key strength of trigonometry lies: even if we scale the triangle to twice its size, the values of the trigonometric functions (csc x among them) will not change.
The Sine Function
The sine function is basically a ratio dependent on the opposite side to the hypotenuse. In order to calculate the sine of a 45°angle, we can use the 45°-45°-90° triangle. Note that we cannot have a square root in the denominator, so we multiply both top and bottom by square root of 2 that removes the square root in the denominator. This is referred to as rationalizing the denominator.
Solved Examples Using Cosec x Formula
Example: Calculate Cosec X if Sin x = 5/9
As Cosec X = 1/ Sin X
So, Cosec X = 9/5