What is the reciprocal of sine known as?

The reciprocal of sine is known as cosecant. In trigonometric functions, each function has a corresponding reciprocal. For sine, which is defined as the ratio of the opposite side to the hypotenuse in a right triangle, its reciprocal—cosecant—represents the ratio of the hypotenuse to the opposite side. Thus, if we denote sine as sin(θ), the cosecant is expressed as csc(θ) = 1/sin(θ). This relationship is fundamental in trigonometry and helps in solving various mathematical problems involving angles and triangles.

Cosecant's role becomes particularly important in the context of trigonometric identities and equations, making it a critical function to understand for anyone studying trigonometry or surveying. The other options represent the reciprocals of different trigonometric functions: secant is the reciprocal of cosine, cotangent is the reciprocal of tangent, and tangent itself is defined as the ratio of sine to cosine. Hence, recognizing cosecant as the reciprocal of sine is essential in navigating these relationships within trigonometric functions.