Reciprocal Trigonometric Functions

Trigonometric functions are the part of mathematics association through angles, triangles. Exclusively there are six trigonometry functions such as sine, cosine, and tangent which are shortening as sin, cos, and tan likewise. The supplementary trigonometric functions are secant, cosecant, and cotangent functions.  These functions are recognized as the reciprocal trigonometric functions.

Understanding Reciprocal Identities is always challenging for me but thanks to all math help websites to help me out.

Reciprocal trigonometric functions:

Within a right triangle, one angle is ninety degree and the face across as of this angle is identified as the hypotenuse. The two faces which appearance the ninety degree angle are described the legs of the right triangle. We illustrate a right triangle below. The legs are identifying as any opposite otherwise adjacent the angle A.





In the above figure we define the following trigonometric functions ratios.

sin(A) = opposite / hypotenuse

cos(A) = adjacent / hypotenuse

tan(A) = opposite / adjacent

Three additional trigonometric ratios can be identifying as the reciprocals of these essential ratios. They are cosecant, secant, and cotangent.

The ratios are specified through the subsequent equations.


cosec(A) = hypotenuse / opposite

sec(A) = hypotenuse / adjacent

cot(A) =  adjacent / opposite

Examples for Reciprocal trigonometric functions

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Example 1 for reciprocal trigonometric functions

In the following figure the angle of A is 45 degree the adjacent side of the right triangle is 15 then computes the opposite side of the triangle



Solution

The adjacent side of the triangle is 15 then to compute opposite side of the triangle using cotangent ratio.

`cot(A) = (adjacent )/ (opposite)`



`cot 45^0 = 15/x`


`x = 15 /cot 45^0`

`x = 15 / 1 `{Since the value of cot 45 degree is 1 }

x = 15

Therefore the opposite side of the triangle is 15

Example 2 for reciprocal trigonometric functions

In the triangle the angle A is 30 degree and opposite side of the right triangle is 12 then computes the hypotenuse side of the triangle





Solution

The opposite side of the triangle is 12 then to compute hypotenuse side of the triangle

Cosec (A) = `"hypotenuse" /" opposite"`

`cosec 30^0 = x/12`

`x = 12 xxcosec 30^0`

x = 12 x 2             {since the value of cosec 30 degree is 2 }

x = 24

Therefore the hypotenuse side of the triangle is 24