Tangent of angle in radians
Find the tangent of a radian angle without switching modes: π/4 gives exactly 1, with sine and cosine both 0.707106781187. Angles where the cosine is effectively zero are refused instead of shown as a huge number. Free in your browser.
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Worked example
- Angle
- 0.7853981634
- Angle
- 0.7853981634 radians
- Sin
- 0.7071067812
- Cos
- 0.7071067812
- Tan
- 1
The tangent of an angle measured in radians is the ratio of sine to cosine of that same angle. Physics, engineering, and calculus almost always express phase, rotation, and angular displacement in radians, so a calculator that assumes degrees by default forces an extra conversion step and invites silent off-by-π errors. This tangent-of-angle-in-radians calculator accepts a single finite angle θ in radians, returns sin(θ), cos(θ), and tan(θ) = sin(θ)/cos(θ), and explicitly marks the result undefined near odd multiples of π/2 where cosine vanishes and the real tangent has a vertical asymptote. Failed validation is not billed.
What tan(θ) in radians means and where it is undefined
On the unit circle an angle θ in radians measures arc length from the positive x-axis. The coordinates of the point on the circle are (cos θ, sin θ), and the slope of the ray from the origin through that point is exactly sin θ divided by cos θ—the geometric definition of tangent. The identity tan θ = sin θ / cos θ is therefore both the computational recipe and the geometric slope.
That recipe fails precisely when cos θ is zero, which occurs at the odd multiples of π/2: …, −3π/2, −π/2, π/2, 3π/2, …. At those angles the terminal ray is vertical, the slope is infinite, and real-valued tangent is undefined.
Where a radians-only tangent helps
Classrooms and tutoring platforms use a tangent of angle in radians calculator so learners can check sin-over-cos results for arbitrary radian inputs without first converting from degrees and without calculator mode mistakes. Content sites that rank for tangent of angle in radians calculator benefit from a dedicated SEO landing whose free browser path matches the paid automation path byte-for-byte on the same pure module—distinct search intent from a multi-function sin-cos-tan tool that defaults to degrees. Failed validation does not consume balance.
Keep requests small, pin the rounded tan field in tests, and you get reproducible tangent values for homework, LMS plugins, and edge workers without standing up symbolic math infrastructure of your own.
What you can do with it
Classroom and homework checks
Let students submit θ in radians and verify tan(θ) = sin(θ)/cos(θ), including clear rejection when the angle is near an odd multiple of π/2.
Phase and signal notebooks
Evaluate tan of a stored radian phase in scripts and APIs without converting to degrees or importing a full CAS library.
FAQ
What happens at π/2 or other odd multiples of π/2?
Cosine is effectively zero there, so real tangent is undefined (vertical asymptote) and the failure is not billed.
Does this accept degrees?
No. The angle is interpreted only as radians. Convert degrees first (degrees × π/180) or use a degrees-aware multi-function tool if you need that mode.
Why return sin and cos as well as tan?
Showing the intermediate sine and cosine makes the sin/cos definition transparent for teaching and debugging, and lets clients recompute the ratio if they want another rounding policy.
What is the tangent of π/4?
The tangent of π/4 is 1. At that angle the sine and cosine are equal, both 0.707106781187, so their ratio is exactly one, the slope of a ray at forty-five degrees.
What is the tangent of π/6?
It is one over the square root of three. Enter π/6 as a decimal in radians and the result appears next to the sine and cosine it comes from, so you can check the ratio yourself.
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/tan-radians \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle":0.785398163397}'const res = await fetch("https://api.kit.forhosting.com/trig/tan-radians", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"angle": 0.785398163397
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/trig/tan-radians",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"angle": 0.785398163397
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/trig/tan-radians", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"angle":0.785398163397}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"angle":0.785398163397}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/trig/tan-radians", 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": 0.785398163397
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "trig.tan_radians",
"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
What tan(θ) in radians means and where it is undefined
Because radian measure is the natural parameter for derivatives and integrals of trigonometric functions, textbooks and numerical libraries default to radians: the derivative of sin θ is cos θ only when θ is in radians. Floating-point cosine is never exactly zero at Math.PI/2, so this capability treats cosine as effectively zero when its absolute value is at most 1e-12 and rejects the request with invalid_input instead of returning a huge finite number that looks like a valid answer. That policy matches classroom language (“undefined at π/2”) and keeps automation from treating an asymptote as a numeric result.
Input contract, response shape, and error behaviour
Extremely large magnitudes beyond the published absolute limit are rejected to avoid meaningless sin and cos evaluations far outside ordinary problem sets. On success the body echoes angle rounded to twelve decimal places for stable goldens across runtimes, sets unit to the literal string radians, returns sin and cos of the angle, returns tan as the quotient sin divided by cos (also rounded), and includes formula as the string tan(θ) = sin(θ) / cos(θ) with a note that θ is in radians. Classic checks: angle equal to zero yields tan equal to zero; angle equal to π/4 (about 0.785398163397) yields tan equal to one; angle equal to π/6 yields tan equal to one over square root of three. If cosine is effectively zero—for example angle equal to π/2—the task fails with a message that tangent is undefined near odd multiples of pi over two. POST a JSON body with one required finite number named angle: the measure of θ in radians, not degrees. Aliases radians, theta, θ, and x are accepted so homework scripts and science notebooks can use familiar field names without remapping. The value may arrive as a JSON number or as a numeric string; missing fields, empty strings, booleans, objects, NaN, and Infinity fail with invalid_input naming the field. Validation failures do not consume prepaid balance. Pair the numeric result with your own conversion if you need degrees; this endpoint never multiplies or divides by π/180 and never assumes a degree default.
Where a radians-only tangent API earns its keep
Exam generators and LMS auto-graders need a deterministic oracle that rejects π/2-class asymptotes as invalid_input instead of inventing Infinity that some graders stringify inconsistently. Signal-processing and control notebooks already store phase in radians; calling a tiny parse API avoids pulling a full computer-algebra system for a single-ratio evaluation and documents the singularity policy next to the number.
Integration use cases
Exam and LMS auto-grading
Mark radian-tangent items with a deterministic oracle that treats cos≈0 asymptotes as invalid_input rather than ±Infinity.
Technical questions
How do I compute the tangent of an angle in radians?
Send a finite number angle (radians). The API returns tan = sin(angle)/cos(angle), plus sin, cos, unit "radians", and the formula string.
What does the tangent of angle in radians calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.