Trigonometric Ratio: Cosecant

Trigonometric Ratio: Cosecant

How to solve cosecant (trigonometric ratio) problems: definition, example, and its solution.

Definition

csc A = 1/sin A = (Hypotenuse) / (Opposite side)

Cosecant is the reciprocal of sine.

Sine: SOH.
[sin A = (Opposite side) / (Hypotenuse)]

So csc A = (Hypotenuse) / (Opposite side).

Example

Find csc A. For a right triangle: Hypotenuse: 4, Adjacent side: 3

csc A = (hypotenuse) / (opposite side)

In the given right triangle,
the opposite side is missing.

So find the opposite side
by using the Pythagorean theorem.

(opposite side) = √7

csc A = 1 / sin A

Sine: SOH.
So sin A = √7/4.

So, its reciprocal, cosecant is
csc A = 4/√7.

Rationalizing a denominator