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.
The Secant Calculator computes the secant of any angle. Enter an angle in degrees or radians and instantly receive sec(x) = 1/cos(x) with the cosine value, step-by-step breakdown, and a reference table of common secant values.
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
- Enter an angle value in the input field.
- Select degrees or radians as the angle unit.
- The calculator instantly computes the secant result.
- Review the cosine value, secant result, and step-by-step explanation.
The Formula
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°).
- Step 1: First compute cos(60°) = 0.5.
- Step 2: Apply the formula: sec(60°) = 1 / cos(60°) = 1 / 0.5.
- Step 3: Therefore sec(60°) = 2.
- 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.