Cosecant Formula

Cosecant is one of the six basic trigonometric ratios and its formula is cosecant(θ) = hypotenuse/opposite, it is also represented as, csc(θ). It is the inverse(reciprocal) ratio of the sine function and is the ratio of the Hypotenus and Opposite sides in a right-angle triangle.

In this article, we have covered, in brief, trigonometric ratios, the Cosecant Formula, related examples and others.

Trigonometric ratios are ratios of sides in a triangle and there are six trigonometric ratios. In a right-angle triangle, the six trigonometric ratios are defined as:

1. sin θ = (Opposite Side/Hypotenuse = AB/AC
2. cos θ = Adjacent Side/Hypotenuse = BC/AC
3. tan θ = Opposite side/adjacent side = AB/BC
4. cosec θ = 1/sin θ = Hypotenuse/Opposite Side = AC/AB
5. sec θ = 1/cos θ = Hypotenuse/Adjacent Side = AC/BC
6. cot θ = 1/tan θ = Adjacent Side/Opposite Side = BC/AB

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 the 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

Article Related to Cosecant Formula:

• Trigonometric Identites
• Trigonometric Function
• Trigonometric Table
• Sin Cos Tan values

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

What is the rule for cosecant?

Rule for cosecant states that cosecant is equal to the ratio of the hypotenuse and perpendicular and is resiprocal of sine function and is represented as, csc x = 1/sin x.

How to calculate the csc?

Cosec is calculated using the formula, cosec A = Hypotenuse / Opposite Side

Is cosecant equal to Cos?

No, cosecant is not equal to cos.

What is cosecant equal to?

Cosecant is written as, csc and is the reciprocal of the sine of an angle. It is equal to the ratio of the hypotenuse to the opposite side of an angle.