What is CSC trigonometry?

CSC (Cosecant) in trigonometry is the reciprocal of the sine function. In other words, for any angle θ in a right-angled triangle or on the unit circle, the cosecant of θ is defined as:

CSC(θ) = 1 / sin(θ)

Where:

sin(θ) is the sine of the angle θ, which is the ratio of the length of the opposite side to the hypotenuse in a right triangle.
For example: If sin(θ) = 0.5, then CSC(θ) = 1 / 0.5 = 2.

In terms of the unit circle, where the sine of an angle θ is the y-coordinate of the point on the unit circle corresponding to θ, the cosecant is the reciprocal of that y-coordinate.

Important Properties of CSC:

CSC(θ) is undefined when sin(θ) = 0, because division by zero is undefined.
The function is periodic, meaning it repeats values at regular intervals. It has a period of 2π (in radians).
Key Trigonometric Identities Involving CSC:

CSC(θ) = 1 / sin(θ)
CSC²(θ) = 1 + cot²(θ), based on the Pythagorean identity sin²(θ) + cos²(θ) = 1.
This function is useful in solving various trigonometric equations and simplifying expressions in trigonometry.