Cosecant Calculator — csc(θ)
Calculate csc(θ) — the cosecant of any angle — by entering degrees or radians. Also displays sin, cos, tan, sec, and cot, with a step-by-step solution and a curve of csc(x) near your angle.
Angle unit
csc(θ) = 1 / sin(θ)
Convert angle to radians
Compute sin(θ)
Compute csc(θ) = 1 / sin(θ)
- 1
Convert to radians
45° × π ÷ 180 = 0,785398 - 2
sin(θ)
sin(0,785398) = 0,707107 - 3
csc(θ) = 1 ÷ sin(θ)
1 ÷ 0,707107 = 1,414214
Jak działa ten kalkulator?
csc(θ) = 1 / sin(θ). Enter an angle in degrees or radians; the cosecant is its reciprocal sine. csc is undefined at 0°, 180°, and all integer multiples of 180°, and always has |csc(θ)| ≥ 1. The calculator also shows all six trig functions and a step-by-step derivation.
Wzór
How this is calculated
The cosecant (csc) is the reciprocal of the sine function: csc(θ) = 1 / sin(θ). It is one of the six standard trigonometric functions — the reciprocal pair of sine — and appears in trigonometric identities, wave equations, and solutions to differential equations. Because it is undefined wherever sin(θ) = 0 (at 0°, 180°, 360°, and all multiples of π radians), its graph has vertical asymptotes at those angles, and the function ranges over (−∞, −1] ∪ [1, +∞).
The calculator converts degrees to radians when needed (radians = degrees × π / 180), then computes sin(θ) using the JavaScript Math.sin function (IEEE 754 double precision), and finally divides 1 by that result to get csc(θ). The same angle also yields cos, tan = sin/cos, sec = 1/cos, and cot = cos/sin. Angles where sin = 0 or cos = 0 produce undefined (—) results for the functions that divide by those values.
Practical note: the floating-point representation of irrational angles (e.g., 90° stored as π/2 ≈ 1.5707963…) carries tiny rounding errors. csc(90°) should be exactly 1, but may read as 1.000000000000001 at full precision. The display rounds to six decimal places, which hides those artefacts for everyday use.
Najczęściej zadawane pytania
csc(90°) = 1 / sin(90°) = 1 / 1 = 1. It is the minimum absolute value of cosecant, reached whenever sin(θ) = ±1.
sin(0°) = sin(180°) = 0, and division by zero is undefined. The cosecant function has vertical asymptotes at every integer multiple of 180° (or π radians).
The three reciprocal functions are csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), and cot(θ) = 1/tan(θ) = cos(θ)/sin(θ). Together with the identity csc²(θ) = 1 + cot²(θ), they parallel the Pythagorean identity sin²(θ) + cos²(θ) = 1.
Znany również jako
TG we-Calculate Editorial Team. (2026). Cosecant Calculator — csc(θ) [Online calculator]. TG we-Calculate. https://we-calculate.com/pl/calculator/csc-calculator
TG we-Calculate Editorial Team. "Cosecant Calculator — csc(θ)." TG we-Calculate. 2026. https://we-calculate.com/pl/calculator/csc-calculator.
TG we-Calculate Editorial Team, "Cosecant Calculator — csc(θ)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/pl/calculator/csc-calculator
@misc{wecalculate_csc_calculator, title = {Cosecant Calculator — csc(θ)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/pl/calculator/csc-calculator}}, year = {2026}, note = {TG we-Calculate} }
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