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Cosecant Formula

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Trigonometry is defined as a discipline of mathematics that defines the relationship between the angles and sides of a right-angled triangle. It’s used to figure out the unknown sides of a right triangle, as well as the angles that form between them. We have to determine the remaining sides and angles of a triangle if we are given some data. This is calculated by using the proper ratio of a triangle’s side to its acute angle.

 

Cosecant formula

A trigonometric ratio is defined as the ratios of acute angles or respective opposite sides. The cosecant formula says that the ratio of the length of the hypotenuse and the side opposite the angle gives us the cosecant ratio. It is denoted by cosec θ. It is the reciprocal of sine trigonometric ratio, that is, equal to 1/sin θ. If θ is the angle that lies between the hypotenuse and base of a right-angled triangle then,

cosec θ = Hypotenuse/Perpendicular = 1/sin θ

Sample Problems

Problem 1: If sin x = 3/5, find the value of cosec x using the formula.

Solution:

We have, sin x = 3/5.

Using the formula we get,

cosec x = 1/sin x

= 1/(3/5)

= 5/3

Problem 2: If cos x = 12/13, find the value of cosec x using the formula.

Solution:

We have, cos x = 12/13.

So we get, sin x = 5/13.

Using the formula we get,

cosec x = 1/sin x

= 1/(5/13)

= 13/5

Problem 3: If tan x = 12/5, find the value of cosec x using the formula.

Solution:

We have, tan x = 12/5.

So we get, sin x = 12/13 and cos x = 5/13.

Using the formula we get,

cosec x = 1/sin x

= 1/(12/13)

= 13/12

Problem 4: If sin x = 8/17, find the value of cosec x using the formula.

Solution:

We have, sin x = 8/17.

Using the formula we get,

cosec x = 1/sin x

= 1/(8/17)

= 17/8

Problem 5: If cot x = 15/8, find the value of cosec x using the formula.

Solution:

We have, cot x = 15/8.

So we get, cos x = 15/17 and sin x = 8/17.

Using the formula we get,

cosec x = 1/sin x

= 1/(8/17)

= 17/8

Problem 6: If sin x = 12/13, find the value of cosec x using the formula.

Solution:

We have, sin x = 12/13.

Using the formula we get,

cosec x = 1/sin x

= 1/(12/13)

= 13/12

Problem 7: If sec x = 5/3, find the value of cosec x using the formula.

Solution:

We have, sec x = 5/3.

So we get, cos x = 3/5 and sin x = 4/5.

Using the formula we get,

cosec x = 1/sin x

= 1/(4/5)

= 5/4


Last Updated : 30 Dec, 2023
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