Csc calculator
Get the cosecant of any angle in degrees or radians: csc 30° is 2, because the sine of 30° is 0.5. Angles where the sine is zero, such as 0° and 180°, are refused instead of producing an infinite answer. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Angle
- 30
- Degrees
- 30 degrees
- Radians
- 0.5235987756
- Sine
- 0.5
- Cosecant
- 2
Cosecant is the reciprocal of sine: csc of theta equals one over sin of theta, provided sine is not zero. Students meet it when rewriting one over sine in identities, when a reciprocal trigonometric form is required in a textbook table, or when a waveform or surveying formula already uses csc instead of a rewritten sine.
What cosecant means and when the reciprocal is undefined
Cosecant is the reciprocal trigonometric function defined by csc of theta equals one over sine of theta, whenever sine is not zero. On the unit circle that is the reciprocal of the signed vertical coordinate of the point at angle theta, so the value is large when the point is near the x-axis and equals one or minus one at the top and bottom of the circle.
Unlike sine, which is defined at every real angle, cosecant has vertical asymptotes at every integer multiple of one hundred eighty degrees, the same family as k times pi radians: there the height is zero and dividing by that height is undefined. That is why this page exists as its own landing rather than as a footnote on a sine calculator: people search for csc or a csc calculator when they need the reciprocal and an honest refusal at those poles, not Infinity and not a silent NaN.
Degrees are converted to radians with the identity that radians equal degrees times pi over one hundred eighty before the library sine runs; forgetting that conversion is the usual classroom bug, because sine of thirty radians is about minus zero point nine eight eight, whose reciprocal is not two.
Special angles have textbook exact reciprocals that students expect without a trail of nines: cosecant of thirty and one hundred fifty degrees is two, cosecant of forty-five and one hundred thirty-five degrees is root two, cosecant of sixty and one hundred twenty degrees is two over root three, and cosecant of ninety degrees is one. Negative angles are legal and use oddness: csc of minus theta equals minus csc of theta.
Angles larger than a full turn remain valid and are reduced modulo three hundred sixty degrees only when matching those special values, while the echoed input keeps the original measure. Related searches such as a six-function sine-cosine-tangent table, a combined secant-cosecant-cotangent page, or a sine-only degrees calculator, are different intents. Here the contract is the scalar cosecant of one finite angle in degrees or radians.
Where a dedicated csc calculator earns its keep
Classrooms and tutoring platforms use a csc calculator so learners can check the reciprocal of sine of an arbitrary classroom angle without mixing degrees and radians or copying a calculator mode they cannot see. Exam generators need a deterministic oracle that marks non-finite tokens and zero-sine poles as invalid instead of silently returning NaN or Infinity, which many language runtimes do and which a buggy grader might treat as a number. Failed validation does not consume balance.
Keep requests small, pin the rounded cosecant in tests, and you get a reproducible csc of an angle for homework, LMS plugins, and edge workers without standing up symbolic math infrastructure of your own.
Related searches such as inverse sine in degrees, a unit-circle explorer, or a full sine-cosine-tangent table that also names secant and cotangent, are different problems and are served by other pages; this contract stays on cosecant of one finite angle so the landing matches what a student actually types when the question is simply csc of this many degrees or radians.
What you can do with it
Classroom and homework checks
Let students submit an angle in degrees or radians and verify csc(θ) = 1/sin(θ), including the identities csc(30°)=2 and csc(90°)=1, against textbook methods.
Exam and LMS auto-grading
Mark cosecant items with a deterministic oracle that rejects angles where sine is zero and never invents Infinity as a successful csc.
Headings, waves, and reciprocal ratios
Convert a degree or radian heading to one over the opposite-over-hypotenuse ratio in robotics, surveying, or signal scripts without importing a full computer-algebra library.
FAQ
When is cosecant undefined?
When the sine of the angle is zero: 0°, 180°, 360°, π radians, and every other integer multiple of 180° (k·π).
Does the csc calculator accept degrees and radians?
Yes. Unit defaults to degrees. Set unit to radians when the number is already a radian measure. Sending thirty with unit radians is not the same as thirty degrees: csc(30°) is 2, while csc(30 rad) is 1/sin(30).
How is this different from a six-function or secant-cosecant page?
Those pages return several functions at once and often refuse an angle if any companion (tan, sec, cot) is undefined. This landing answers only csc of one angle, so 90° succeeds with cosecant 1 even though tangent is undefined there.
What are the cosecants of 30, 60 and 90 degrees?
csc 30° is 2, csc 60° is 2/√3 and csc 90° is exactly 1. Other special angles also come back as clean textbook values, without a trail of nines, so they match the tables in a math book.
Can I enter a negative angle?
Yes. Cosecant is an odd function, so the cosecant of -30° is -2, the opposite of csc 30°. Angles larger than a full turn are accepted too, and the angle you typed is shown back unchanged.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/math/csc \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle":30}'const res = await fetch("https://api.kit.forhosting.com/math/csc", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"angle": 30
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/csc",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"angle": 30
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/csc", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"angle":30}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"angle":30}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/csc", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"angle": 30
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.csc",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Most programming libraries expose only a sine of radians and never a dedicated cosecant, so a caller who thinks in degrees must convert first and then invert, and a caller who lands on a multiple of one hundred eighty degrees must be told the value does not exist rather than being handed Infinity, which JSON cannot represent. This calculator accepts one finite angle in degrees by default, or in radians when you say so, converts if needed, evaluates sine, and returns the reciprocal. When sine is zero the task fails with invalid_input.
Input contract, response shape, and error behaviour
Unit values outside the closed set degrees or radians fail the same way. Ninety degrees is accepted: sine is one and cosecant is one. That is a product difference from a six-function calculator that must refuse ninety because tangent and secant blow up there. On success the body echoes the cleaned angle and the resolved unit, returns degrees and radians for both measures, returns sine as the intermediate, and returns cosecant as the primary result. Example: angle thirty in degrees yields sine one half and cosecant two, because thirty degrees is pi over six radians and one over one half is two. Example: angle ninety yields sine one and cosecant one. Example: angle pi over two with unit radians yields the same pair. POST a JSON body with the required field angle, a finite real number. The field may arrive as a JSON number or as a numeric string in decimal or scientific notation; aliases theta, x, and value are accepted when angle is omitted. An optional unit field selects degrees, the default, or radians; aliases angle_unit and mode are accepted. Missing fields, empty strings, non-numeric text, NaN, and Infinity fail with invalid_input naming the field and are not billed. Cosecant is undefined when sine is zero, so zero degrees, one hundred eighty degrees, three hundred sixty degrees, pi radians, and the rest of that lattice fail with invalid_input rather than returning Infinity, which JSON cannot represent. A formula string restates csc of theta equals one over sin of theta, a compact expression such as csc(30°), and a one-line message complete the payload. Pair the payload with your own labels; this endpoint does not emit plots, a secant or cotangent companion, or a step-by-step lesson beyond the formula field.
Where a dedicated csc calculator earns its keep
Surveying, robotics, and wave scripts sometimes store headings in degrees and still need one over the opposite-over-hypotenuse ratio; calling a tiny parse API avoids pulling a computer-algebra system for one conversion, one sine, and one reciprocal.
Technical questions
How do I compute the cosecant of an angle?
Send a finite number in the field angle (aliases theta, x, value) and optionally unit as degrees (default) or radians. The API converts if needed, evaluates sine, and returns cosecant as 1/sin(θ).
What does the csc calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.