Compute sec(θ) = 1/cos(θ) for single or thousands of angles. Degrees or radians. Upload CSV/TXT. Download results instantly.
🔢 Launch Calculator ↓Paste hundreds or thousands of angles, one per line. Process them all with a single click — no waiting, no limits.
Drag and drop or browse for your .csv or .txt file. Angles are loaded into the bulk processor instantly.
Single-angle mode shows full trig context: cos(θ), sin(θ), tan(θ), csc(θ), cot(θ), arcsec and more.
Real-time validation catches non-numeric inputs and flags undefined sec(θ) values (at 90°, 270°, etc.) clearly.
After each calculation, view count, min, max, and mean sec(θ) instantly in the summary dashboard.
Copy to clipboard or download a ready-to-use CSV with all angles and computed values in one click.
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.csv or .txt · max 5 MB · one angle per line
Or paste angles (one per line):
| # | Angle | Unit | sec(θ) | cos(θ) | sin(θ) | tan(θ) | Status |
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The secant function, written as sec(θ), is one of six fundamental trigonometric functions and is defined as the reciprocal of cosine: sec(θ) = 1 / cos(θ). In a right-angled triangle, this translates to the ratio of the hypotenuse to the adjacent side — the inverse of what cosine describes. While it may appear less frequently than sine or cosine in introductory courses, secant is indispensable in calculus, integral evaluation, wave mechanics, and advanced geometry.
Secant's most important identity stems directly from the Pythagorean trigonometric identities. Since sin²(θ) + cos²(θ) = 1, dividing every term by cos²(θ) yields the secant-tangent identity: 1 + tan²(θ) = sec²(θ). This relationship is essential for integral transformations, particularly when evaluating integrals involving √(1 + x²) using trigonometric substitution with x = tan(θ).
The domain of secant excludes all angles where cos(θ) = 0, namely θ = 90° + n·180° (or π/2 + nπ in radians) for any integer n. At these points, sec(θ) is undefined — the function shoots towards positive or negative infinity. Outside these points, the range of sec(θ) is (−∞, −1] ∪ [1, +∞), meaning it never lies between −1 and 1.
Memorising benchmark secant values is a shortcut for examinations and real-world calculations. sec(0°) = 1, sec(30°) = 2/√3 ≈ 1.1547, sec(45°) = √2 ≈ 1.4142, sec(60°) = 2, sec(90°) = undefined, sec(120°) = −2, sec(180°) = −1. Secant is an even function, so sec(−θ) = sec(θ), and it has a period of 360° (2π radians).
Our tool operates in two modes. Single Angle Mode: type your angle, select degrees or radians, choose your desired decimal precision (up to 15 places), and click Compute sec(θ). You immediately see sec(θ) alongside a comprehensive related-numbers panel showing cos(θ), sin(θ), tan(θ), csc(θ), cot(θ), arcsec(θ), and more — similar in scope to professional platforms like Omnicalculator. Bulk Mode: paste up to thousands of angles (one per line) or upload a .csv or .txt file. The tool validates, processes, and displays all results in a sortable table with per-row status badges and a summary statistics bar.
In calculus, the derivative of sec(x) is sec(x)·tan(x), and its integral is the classical result ∫ sec(x) dx = ln|sec(x) + tan(x)| + C. This integral appears routinely when evaluating arc-length formulas and solving differential equations in physics and engineering. The secant-squared function, sec²(x), is the derivative of tan(x), making it central to integration by substitution techniques.
Secant is more than a textbook function. In optics, the secant law describes how light path length through an atmosphere increases as the zenith angle grows — direct application of sec(θ) = path length / vertical thickness. In civil engineering, banked road curves and inclined structural forces involve secant calculations for load distribution. In satellite communications, link-budget calculations use secant to account for atmospheric path at low elevation angles. In machine learning, the secant method (a quasi-Newton root-finding algorithm) uses secant-line approximations to iteratively converge on function roots without requiring explicit derivatives — useful when evaluating complex loss landscapes.
The three reciprocal trig functions — secant, cosecant, and cotangent — are often grouped together. sec(θ) = 1/cos(θ), csc(θ) = 1/sin(θ), and cot(θ) = 1/tan(θ) = cos(θ)/sin(θ). Together with the Pythagorean identities (1 + tan²θ = sec²θ and 1 + cot²θ = csc²θ), these form a complete toolkit for trigonometric simplification and proof-writing. Whether you are verifying identities, computing integrals, or pre-computing lookup tables for embedded systems, this free bulk secant calculator delivers precise, exportable results in seconds — no installation, no account, no limits.
Period: 360° (2π rad) · Range: (−∞, −1] ∪ [1, +∞) · Even function: sec(−θ) = sec(θ)
Type a single angle or paste a list (one per line). Alternatively, drag and drop or upload your .csv / .txt file.
Select degrees or radians and pick your decimal precision from 2 up to 15 places for maximum accuracy.
Click Compute. View the results table with status badges, then clear, copy to clipboard, or download as CSV.
Secant is defined as sec(θ) = 1/cos(θ) = Hypotenuse / Adjacent. It is the reciprocal of the cosine function. Its range is (−∞, −1] ∪ [1, +∞), and it is undefined at angles where cosine equals zero (90°, 270°, etc.).
Either type a single angle in the Single Angle card, or paste multiple angles (one per line) in the Bulk Angles card, or upload a .csv / .txt file. Select your unit (degrees or radians) and decimal precision, then click the compute button. Results appear in the section below.
sec(θ) is undefined whenever cos(θ) = 0 — that is at θ = 90°, 270°, 450°, −90°, etc. (π/2, 3π/2, 5π/2, −π/2 in radians). The calculator labels these rows as UNDEFINED with a red badge.
Yes. Prepare a .csv or .txt file with one angle value per line — no header row needed. Files up to 5 MB are accepted. Upload via drag-and-drop or the file picker. All values are validated and processed instantly in your browser.
Completely free, no registration required. All calculations run client-side in your browser using JavaScript — no data is ever transmitted to a server. Your angles stay private.
This is derived from the Pythagorean identity sin²(θ) + cos²(θ) = 1 by dividing both sides by cos²(θ). It results in tan²(θ) + 1 = sec²(θ). This identity is used extensively in calculus for trigonometric substitution in integration problems.
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