Secant of an Angle in Degrees Calculator
Type an angle in degrees and see its secant next to the cosine it comes from: 60° has a cosine of 0.5, so its secant is 2. Angles such as 90° and 270° are flagged instead of giving a huge false number. Free in your browser.
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- Your data stays on your device
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Worked example
- Angle
- 60
- Angle degrees
- 60
- Cosine
- 0.5
- Secant
- 2
This secant of an angle in degrees calculator evaluates secant directly from the familiar degree measure used in geometry, engineering, surveying, and classroom exercises. Enter one finite angle and receive its cosine together with the corresponding secant, calculated as one divided by cosine. The calculator also identifies angles where cosine is zero, because secant has no defined real value at those points. Results are rounded consistently for readable output while the original angle is preserved, making the response convenient for both quick checks and automated workflows.
How to calculate secant from an angle in degrees
Secant is the reciprocal of cosine, so the defining relationship is secant of theta equals one divided by cosine of theta. This calculator accepts theta in degrees, converts that measure to radians for the underlying trigonometric operation, evaluates cosine, and then takes its reciprocal. For example, cosine of 60 degrees is 0.5, so secant of 60 degrees is 2.
The response includes the supplied angle, the computed cosine, and the resulting secant, allowing you to inspect every important part of the calculation. You may enter positive angles, negative angles, angles larger than one full turn, or decimal values. Trigonometric functions are periodic, which means adding or subtracting 360 degrees does not change the cosine or secant.
A value such as 420 degrees therefore has the same secant as 60 degrees. Use ordinary numeric degree values without a degree symbol, equation text, or units in the input field. The calculator rejects missing values, text, infinity, and other inputs that cannot represent a finite angle.
Why secant can be undefined
A reciprocal cannot be formed when its denominator is zero. Because secant is one divided by cosine, secant is undefined whenever cosine equals zero. In degree measure, that occurs at 90 degrees and 270 degrees, and at every coterminal angle reached by adding or subtracting any multiple of 360 degrees.
An equivalent general pattern is 90 degrees plus any integer multiple of 180 degrees. The calculator detects those angles explicitly and returns a clear input error instead of displaying an enormous misleading number. This explicit check matters because computer arithmetic represents pi approximately: a direct software calculation of cosine at 90 degrees can produce a tiny residual close to zero rather than exact zero.
Taking the reciprocal of that artifact would suggest a huge finite secant even though the mathematical function is undefined. Angles merely near 90 or 270 degrees are valid, however, and their secants can be very large in magnitude. That behavior is expected because cosine approaches zero as the angle approaches one of these vertical asymptotes.
Reading and using the result responsibly
Familiar angles may have exact radical forms: for example, secant of 45 degrees is the square root of 2, while the calculator returns its decimal approximation. Keep additional precision requirements in mind when results feed sensitive numerical simulations or repeated downstream operations. The sign of secant always matches the sign of cosine.
It is positive in quadrants I and IV and negative in quadrants II and III, while remaining undefined on the boundaries where cosine is zero. You can use the included cosine field to verify that relationship or to explain the result in a worked solution.
What you can do with it
Check trigonometry homework
Confirm a degree-based secant result and inspect the cosine used to obtain it.
Validate engineering calculations
Calculate a stable decimal secant for finite angles used in formulas and data checks.
Detect undefined domain points
Identify angles where cosine is zero before a reciprocal enters a larger workflow.
FAQ
What formula does the calculator use?
It uses secant of theta equals one divided by cosine of theta, with theta interpreted in degrees.
When is secant undefined?
Secant is undefined at 90 degrees plus any integer multiple of 180 degrees because cosine is zero there.
Can I enter a negative angle?
Yes. Any finite positive, negative, zero, or decimal degree value is accepted.
Why is the result rounded?
Cosine usually produces an irrational decimal. Rounding to twelve decimal places keeps output readable and deterministic.
What is the secant of 60 degrees?
The secant of 60° is 2. The cosine of 60° is 0.5, and the secant is one divided by the cosine, so one divided by 0.5 gives exactly 2.
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/sec-degrees \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle":60}'const res = await fetch("https://api.kit.forhosting.com/trig/sec-degrees", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"angle": 60
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/trig/sec-degrees",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"angle": 60
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/trig/sec-degrees", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"angle":60}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"angle":60}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/trig/sec-degrees", 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": 60
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "trig.sec_degrees",
"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
Reading and using the result responsibly
The returned cosine and secant are rounded to twelve decimal places to provide stable, readable JSON values. This precision is suitable for most educational work, routine engineering estimates, spreadsheets, validation rules, and application interfaces, but it should not be mistaken for symbolic exactness. For automated use, send one angle per request and handle the invalid input response as a mathematical domain condition, not as a transient service failure. Each API request costs $0.002, and the same deterministic calculation produces the same rounded output for the same valid input.
Technical questions
How much does an API request cost?
Each request costs $0.002.