Secant Calculator

How to Calculate Secant

The secant function, denoted as sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function. It is widely used in various fields of mathematics, physics, and engineering.

Formula

The secant of an angle θ is defined as:

\[ \sec(\theta) = \frac{1}{\cos(\theta)} \]

Where:

• sec(θ) is the secant of the angle θ
• cos(θ) is the cosine of the angle θ
• θ is the angle in radians

Calculation Steps

1. Ensure the angle is in radians. If it's in degrees, convert it to radians by multiplying by π/180°.
2. Calculate the cosine of the angle using a calculator or trigonometric tables.
3. Take the reciprocal of the cosine value to get the secant.

Example

Let's calculate sec(60°):

1. Convert 60° to radians: 60° × (π/180°) = π/3 radians
2. Calculate cos(π/3) ≈ 0.5
3. Calculate sec(π/3) = 1 / cos(π/3) = 1 / 0.5 = 2

Therefore, sec(60°) = 2

Visual Representation

This diagram illustrates sec(60°). The blue line represents the angle of 60°, and the red line shows the secant value of 2 on the x-axis.