Cosecant

For an acute angle θ of a right triangle, the cosecant of θ is the ratio between the lengths of the hypotenuse and the opposite side.

The cosecant of θ is written as csc(θ).

This trigonometric ratio states the ratio between the hypotenuse and the opposite side to a certain angle. It gives no indication about the lengths of the sides.

When the opposite side and hypotenuse lengths change for a given angle, if their ratio stays the same then the cosecant, too, would stay the same. Also note that the cosecant of θ is the reciprocal of the sine of θ. csc θ=hyp/opp sin θ =opp/hyp ⇒ csc θ = 1/sin θ