Calculate the cosecant (1/sin) of an angle in degrees or radians with undefined-angle detection.
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Trigonometry
The cosecant calculator computes csc(θ) = 1/sin(θ) for any angle. It flags undefined values at 0°, 180°, and other angles where sine is zero.
Cosecant is the reciprocal of sine: csc(θ) = 1/sin(θ). It is undefined wherever sine equals zero — at integer multiples of 180° (0°, 180°, 360°, ...).
Cosecant values are always greater than or equal to 1 or less than or equal to -1. The function never takes values between -1 and 1.
Common exact values: csc(30°) = 2, csc(45°) = sqrt(2) approx 1.414, csc(60°) = 2sqrt(3)/3 approx 1.155, csc(90°) = 1.
Frequently asked questions
1. sin(90°) = 1, so csc(90°) = 1/1 = 1.
Cosecant is the reciprocal of sine: csc(x) = 1/sin(x). Arcsin is the inverse function: it returns the angle whose sine equals a given value. They are different operations.
Related
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Calculate the arccosine (inverse cosine) of a value and return the angle in degrees and radians with exact fractions of pi.
