Sine function calculator
Find y for the general sine y = a·sin(bx + c) at the x you choose: amplitude 2, frequency 1 and phase 0 give 0 at x zero. Phase works in radians and negative values are honoured. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Amplitude
- 2
- Frequency
- 1
- Phase
- 0
- X
- 0
- Argument
- 0
- Y
- 0
The general sine function y equals a times the sine of bx plus c is the standard transformed sine that algebra and precalculus courses graph, tabulate, and evaluate at a chosen point. Amplitude a stretches the wave vertically, the frequency coefficient b compresses or stretches it along the x-axis, and phase c is added to the argument before sine is taken. Given those three coefficients and a finite independent value x, this calculator returns the single number y. It does not invert the sine, extract a period from a sketch, convert a bare angle from degrees, or add a vertical midline — it evaluates the closed form y = a·sin(bx + c) with one deterministic sine.
What y = a·sin(bx + c) means at a point
The sine function in general form is written y equals a times the sine of the quantity bx plus c. The coefficient b is the frequency factor that multiplies x inside the argument; the period of one full cycle is two-pi divided by the absolute value of b whenever b is not zero. The horizontal shift of the graph, if you prefer that language, is negative c over b when b is not zero.
Evaluating the function at a point is then a three-step arithmetic job: form the argument bx plus c, take the sine of that argument in radians, and multiply by the amplitude a. This capability does exactly that and returns y. It is not a unit-circle lookup of sine of a lone angle, not a wave model that takes a period T and a vertical offset k, and not a solver that extracts A, B, and C from a sketch.
Send four finite numbers and receive the function value. When a is zero every x maps to y equals zero, which is the zero function and is equally valid. Signs are honoured throughout: a negative amplitude reflects the graph through the x-axis, and a negative frequency reverses the direction of the oscillation without changing the absolute period.
What you enter and what you get back
Amplitude is the leading coefficient a in y equals a sine of bx plus c. Frequency is the coefficient b that multiplies x — not a Hertz reading from a laboratory analyzer, but the same b that appears in every textbook statement of the general sine function. Phase is the constant c added inside the argument, measured in radians.
The independent variable x is the point at which you want the value. Nothing else is required: there is no degree-versus-radian switch on x, and there is no optional vertical shift. On success the body includes the echoed inputs, the intermediate argument bx plus c, the formula string y = a·sin(bx + c), and the primary result y, all rounded to twelve decimal places so automated goldens compare byte-for-byte across runtimes.
Example: amplitude two, frequency one, phase zero, x zero yields argument zero and y zero. Example: amplitude three, frequency two, phase zero, x equal to pi over four yields argument pi over two and y equal to three.
Where a sine-function evaluator earns its keep
Classrooms use a sine function calculator so students can check a table of values for y equals a sine of bx plus c without a graphing calculator that hides the intermediate argument. Exam-prep generators need a deterministic oracle that marks a point evaluation against a known y and rejects non-numeric garbage instead of returning NaN that a buggy grader might treat as a number.
Engineering notebooks that already know amplitude, the b coefficient, and phase in the same parameterization can drop the four numbers in and record y next to a lab reading. Failed validation does not consume balance. Keep requests small, pin the rounded y in tests, and you get a reproducible function value for homework, LMS plugins, and edge workers without standing up symbolic math infrastructure of your own.
If you instead need sine of a lone angle in degrees, a wave specified by period and midline, or the amplitude and period extracted from coefficients, use the dedicated sibling calculators rather than stretching this contract.
What you can do with it
Classroom tables for y = a·sin(bx + c)
Let students submit amplitude, frequency, phase, and x and verify the function value against the three-step textbook method of forming bx+c, taking sine, and scaling by a.
Exam and LMS auto-grading
Mark sine-function evaluation items with a deterministic oracle that rejects non-finite coefficients instead of scoring a silent NaN as a numeric answer.
Scripts and lab notebooks
Evaluate a stored envelope y = a·sin(bx + c) at sample points in animation, audio, or lab scripts without importing a computer-algebra library.
FAQ
How do I evaluate y = a·sin(bx + c) at a given x?
Send four finite numbers: amplitude (a), frequency (b), phase (c, radians), and x.
Is frequency the same as Hertz or the period T?
No. Frequency here is the textbook coefficient b in y = a·sin(bx + c). The period of one cycle is 2π/|b| when b is not zero. This is not a period-and-midline sine-wave model.
Are phase and x in degrees or radians?
Radians. Phase c is added to bx before sine, and the sine is the standard radian sine. Convert degrees yourself if your source data is in degrees.
What is the period of y = a·sin(bx + c)?
One full cycle lasts 2π divided by the absolute value of b, as long as b is not zero. With a frequency of 1 the wave repeats every 2π units of x, and a larger b squeezes the cycles closer together.
What happens with a negative amplitude or a negative frequency?
A negative amplitude flips the graph across the x-axis, so every peak becomes a trough. A negative frequency makes the wave run in the opposite direction, but the length of one cycle stays the same.
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/sine-function \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"amplitude":2,"frequency":1,"phase":0,"x":0}'const res = await fetch("https://api.kit.forhosting.com/math/sine-function", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"amplitude": 2,
"frequency": 1,
"phase": 0,
"x": 0
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/sine-function",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"amplitude": 2,
"frequency": 1,
"phase": 0,
"x": 0
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/sine-function", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"amplitude":2,"frequency":1,"phase":0,"x":0}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"amplitude":2,"frequency":1,"phase":0,"x":0}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/sine-function", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"amplitude": 2,
"frequency": 1,
"phase": 0,
"x": 0
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.sine_function",
"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.
Limits
max_abs | 1000000000000 |
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
Missing or non-finite inputs fail with invalid_input and are not billed.
What y = a·sin(bx + c) means at a point
Here a is the amplitude: the greatest distance the graph reaches above or below the x-axis when there is no extra vertical shift. The constant c is the phase: it is added to bx before sine is applied, so a positive c advances the argument and a negative c delays it. When b is zero the expression collapses to the constant a times sine of c, which is still a well-defined sine function, so the request succeeds instead of being rejected.
Input contract, response shape, and error behaviour
POST a JSON object with four fields, each a finite number: amplitude (alias a), frequency (alias b), phase (alias c), and x. Each field may arrive as a JSON number or as a decimal numeric string; empty strings, booleans, objects, NaN, and Infinity fail with invalid_input naming the field. Magnitudes above the published absolute limit of one trillion are also rejected so intermediate IEEE doubles stay finite on the Worker and in the browser. Failed validation does not consume prepaid balance. Pair the numeric y with your own plotting code if you need a sketch of one period; this endpoint evaluates the function at a single x and does not emit graphs or step-by-step prose beyond the formula field.
Where a sine-function evaluator earns its keep
Animation and audio scripts often store envelopes in this exact textbook form and only need y at a sample x; calling a tiny parse endpoint avoids pulling a computer-algebra system for four arithmetic operations and a sine.
Technical questions
What happens if frequency b is zero?
The request succeeds. y = a·sin(c) is a constant function, which is still a well-defined sine function, so the calculator returns that constant rather than an error.
What does the sine function calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.