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
यह कैलकुलेटर कैसे काम करता है?
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.
सूत्र
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.
अक्सर पूछे जाने वाले प्रश्न
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.
इस नाम से भी जाना जाता है
TG we-Calculate Editorial Team. (2026). Cosecant Calculator — csc(θ) [Online calculator]. TG we-Calculate. https://we-calculate.com/hi/calculator/csc-calculator
TG we-Calculate Editorial Team. "Cosecant Calculator — csc(θ)." TG we-Calculate. 2026. https://we-calculate.com/hi/calculator/csc-calculator.
TG we-Calculate Editorial Team, "Cosecant Calculator — csc(θ)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/hi/calculator/csc-calculator
@misc{wecalculate_csc_calculator, title = {Cosecant Calculator — csc(θ)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/hi/calculator/csc-calculator}}, year = {2026}, note = {TG we-Calculate} }
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