Math July 13, 2026 · 8 Min Read

Secant Calculator – Guide & Formulas

Calculate the secant (sec) of any angle instantly. Enter an angle in degrees or radians to find sec(x) = 1/cos(x) with step-by-step results.

Try the free calculator

Put these formulas into practice with our instant, step-by-step Secant Calculator.

Open Calculator ›

Use our free **secant calculator** to compute **sec(x) = 1/cos(x)** for any angle in **degrees or radians**. This **secant of an angle** tool instantly shows the **cosine value**, **secant result**, and **step-by-step breakdown**. Whether you need a **1/cos calculator**, **secant table**, or **trigonometric function calculator** with **common secant values**, this tool provides accurate results. 100% free — no signup required!

Key Takeaway

Use the free Secant Calculator to calculate the secant (sec) of any angle instantly. enter an angle in degrees or radians to find sec(x) = 1/cos(x) with step-by-step results. Get instant results with step-by-step explanations.

How to Use the Secant Calculator

  1. Enter an **angle value** in the input field of the **secant calculator**.
  2. Select **degrees** or **radians** as the angle unit.
  3. The calculator instantly computes **sec(x) = 1/cos(x)**.
  4. Review the **cosine value** used in the calculation.
  5. Check the **secant result** and the **step-by-step explanation**.
  6. Compare with the **common secant values** table for reference.
  7. Use the result in your **trigonometry**, **calculus**, or **physics** calculations.

The Formula

sec(θ) = 1 / cos(θ)

Variable Definitions

  • sec(θ): The secant of angle θ: the reciprocal of cosine
  • θ: The input angle in degrees or radians
  • cos(θ): The cosine of angle θ: adjacent/hypotenuse

Example: Secant of 60°

Find sec(60°).

  1. Step 1: First compute cos(60°) = 0.5.
  2. Step 2: Apply the formula: sec(60°) = 1 / cos(60°) = 1 / 0.5.
  3. Step 3: Therefore sec(60°) = 2.
  4. Step 4: Verify: cos(60°) × sec(60°) = 0.5 × 2 = 1 —

Frequently Asked Questions

What is secant?

Secant (sec) is the reciprocal of the cosine function. For any angle θ, sec(θ) = 1/cos(θ). In a right triangle, it is the ratio of the hypotenuse to the adjacent side.

What is the domain of secant?

The domain of sec(θ) is all real numbers except where cos(θ) = 0, which occurs at θ = 90° + nπ (90°, 270°, 450°, etc.). At these points, sec(θ) is undefined.

What is the range of secant?

The range of sec(θ) is (-∞, -1] ∪ [1, +∞). The secant function never takes values between -1 and 1 exclusive, since |cos(θ)| ≤ 1.

What is sec(0°)?

sec(0°) = 1/cos(0°) = 1/1 = 1. Since cos(0°) = 1, the secant at 0° is also 1.

What is sec(60°)?

sec(60°) = 1/cos(60°) = 1/0.5 = 2. This is one of the most commonly used secant values.

What is sec(90°)?

sec(90°) is undefined because cos(90°) = 0, and dividing by zero is undefined. The secant function has a vertical asymptote at 90°.

How is secant related to cosine?

Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ). Equivalently, cos(θ) = 1/sec(θ). They are inverse multiplicative pairs.

What is the cofunction of secant?

The cofunction of secant is cosecant (csc). The identity is sec(θ) = csc(90° - θ). For example, sec(30°) = csc(60°) = 2/√3 ≈ 1.155.

How do I graph secant?

The graph of sec(θ) has vertical asymptotes wherever cos(θ) = 0 (at 90°, 270°, etc.). Between consecutive asymptotes, the graph forms U-shapes above and below the x-axis, touching y = 1 and y = -1 at the peaks and troughs of cosine.

What are common secant values?

Common values: sec(0°) = 1, sec(30°) = 2/√3 ≈ 1.155, sec(45°) = √2 ≈ 1.414, sec(60°) = 2, sec(90°) = undefined, sec(120°) = -2, sec(180°) = -1.