Csc cosine

Cosecant, written csc, is the reciprocal of sine. Cosine, written cos, is a different trigonometric function. Cosecant is not another spelling of cosine, and the reciprocal of cosine is secant.

Meaning and context

For an angle θ where the denominators are nonzero, csc θ = 1/sin θ and sec θ = 1/cos θ. In a right triangle, sine compares opposite side to hypotenuse, while cosine compares adjacent side to hypotenuse.

Examples and usage

At 30 degrees, sine is one-half, so cosecant is two. Cosine at that angle is √3/2. This example makes the distinction visible: csc 30° and cos 30° do not return the same number.

What to check

Cosecant is undefined wherever sine is zero. Before using a calculator, check whether the angle is in degrees or radians. A correct formula with the wrong angle mode can still produce an incorrect answer.

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