Secant, cosecant & cotangent calculator
Find the three reciprocal trig values at once: at 30° the cosecant is 2 and the secant about 1.1547, shown next to sine, cosine and tangent. Angles where a value has no answer are refused, never shown as infinity. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Angle
- 30
- Radians
- 0.5235987756 degrees
- Sin
- 0.5
- Cos
- 0.8660254038
- Tan
- 0.5773502692
Enter the angle in degrees by default or switch to radians, choose how many decimal places you want, and the engine returns sec, csc, and cot together with sine, cosine, and tangent for context. The path is fully deterministic: no network, no randomness, no clock.
What secant, cosecant and cotangent mean
Secant, cosecant, and cotangent are the classic reciprocal companions of cosine, sine, and tangent. By definition sec θ equals one divided by cos θ, csc θ equals one divided by sin θ, and cot θ equals cos θ divided by sin θ, which is also one over tan θ wherever tan is defined.
Students meet these three names when textbooks expand the six basic functions, when Pythagorean identities are rewritten as one plus tan squared equals sec squared, and when right-triangle problems ask for the ratio of hypotenuse to adjacent or opposite sides. Engineers and analysts use them less often in modern libraries that prefer sin and cos, but they still appear in older CAD notes, surveying formulas, Fourier identity tables, and contest problems that expect the reciprocal form.
This calculator returns the angle you supplied, the unit it was interpreted under, the equivalent radian measure, the three primary values sin, cos, and tan, and the three reciprocal values sec, csc, and cot, all rounded to your requested precision.
Where reciprocal trig fits in study, teaching, and automated checks
Students reach for a secant-cosecant-cotangent calculator when a homework set lists only sec and csc in the answer key, when they must convert a right-triangle ratio into reciprocal form, or when they are checking that one plus cot squared still equals csc squared at a concrete angle before a quiz. Teachers can pre-generate finite answer keys for safe angles without trusting opaque calculator apps that print Infinity, switch to scientific notation, or silently change mode between degrees and radians.
Developers call the same contract from scripts to seed deterministic test vectors for libraries that still expose sec, csc, and cot helpers, to validate survey or optics formulas written in reciprocal language, or to satisfy programming-challenge statements that demand those three outputs rather than only sine and cosine. Contest practice often needs a fast offline source of reciprocal values so solutions can be checked without downloading tables under time pressure.
Pair it with the unit-circle calculator when you only need cos and sin, with the Pythagorean identity verifier when residual checks matter, and with degree-to-radian conversion when mode mistakes are the real bug you are hunting.
What you can do with it
Homework reciprocal-function checks
Look up exact-enough sec, csc, and cot values for textbook exercises that ask for reciprocal forms instead of only sine and cosine.
FAQ
What does the secant-cosecant-cotangent calculator cost?
It is free in your browser on this page.
How are sec, csc, and cot defined?
sec θ = 1/cos θ, csc θ = 1/sin θ, and cot θ = cos θ/sin θ (also 1/tan θ where tan is defined).
What happens at 0° or 90°?
At 0° (and other angles where sin is zero) cosecant and cotangent are undefined. At 90° (and where cos is zero) secant is undefined.
Can I enter the angle in radians?
Yes. Set unit to radians (or rad). The default unit is degrees.
Why does the response also include sin, cos, and tan?
They provide context for the reciprocals and help you verify that sec is 1/cos, csc is 1/sin, and cot is cos/sin at the same angle and precision.
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/trig/secant-cosecant \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle":30}'const res = await fetch("https://api.kit.forhosting.com/trig/secant-cosecant", {
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/trig/secant-cosecant",
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/trig/secant-cosecant", 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/trig/secant-cosecant", 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": "trig.secant_cosecant",
"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
This secant-cosecant-cotangent calculator evaluates the three reciprocal trigonometric functions for a single finite angle: secant as one over cosine, cosecant as one over sine, and cotangent as cosine over sine. When sine or cosine is zero the corresponding reciprocals are undefined through division by zero, so the tool rejects those angles with invalid_input instead of printing Infinity.
What secant, cosecant, and cotangent mean and what the response contains
A short formula string restates the definitions so API consumers and worksheets stay aligned. There is no approximate path presented as Infinity and no silent substitution when a reciprocal blows up: if sin or cos is numerically zero within a tight absolute threshold, the engine raises invalid_input and refuses to invent a finite answer.
How the angle is read, when domains fail, and how precision is applied
After conversion to radians the engine evaluates Math.sin and Math.cos once. The preferred field is angle, but aliases value, theta, x, degrees, and deg are accepted so spreadsheets, query strings, and typed forms can reuse the same contract without renaming columns. Optional unit accepts degrees, deg, radians, or rad, with degrees as the default, and aliases from and input_unit cover common form labels. Precision is an integer from zero through fifteen decimal places with a default of twelve; aliases decimals and dp map to the same control. Missing angle, non-numeric strings, Infinity, and NaN fail immediately with invalid_input. If the absolute value of sine is at or below one times ten to the minus twelve, cosecant and cotangent are undefined and the request is rejected with a message that names division by zero and typical examples such as zero degrees, one hundred eighty degrees, or integer multiples of pi. If cosine is similarly near zero, secant and tangent are undefined and the request fails for angles such as ninety degrees, two hundred seventy degrees, or pi over two plus integer multiples of pi. Only when both sine and cosine are safely away from zero does the engine form sec equals one over cos, csc equals one over sin, cot equals cos over sin, and tan equals sin over cos, then round every numeric field to the requested decimal places while collapsing signed zero so JSON stays clean. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing reciprocal trig yourself.
Where reciprocal trig fits in study, teaching, and automated checks
Product and curriculum teams use the endpoint when building interactive worksheets that must refuse undefined angles with a clear error instead of rendering blank or infinite cells. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic CI fixtures
Generate reproducible secant, cosecant, and cotangent decimals for unit tests without hand-maintaining tables or accepting Infinity.
Teaching demos of undefined domains
Show students that 0°, 90°, and related angles fail cleanly with invalid_input when a reciprocal would divide by zero.