Secant (sec) in mathematics is a trigonometric function that's the reciprocal of the cosine function.
In the context of a right triangle:
- sec(θ) = Hypotenuse / Adjacent
Therefore, the secant of an angle (θ) is the ratio of the length of the hypotenuse to the length of the adjacent side.
Understanding Secant:
- Relationship to Cosine: Since secant is the reciprocal of cosine, we can write: sec(θ) = 1 / cos(θ)
- Unit Circle: On the unit circle, the secant is represented as 1/x, where 'x' is the x-coordinate of the point where the terminal side of the angle intersects the unit circle.
- Domain and Range: The domain of the secant function is all real numbers except for angles of the form (π/2) + nπ, where n is an integer (because cosine is zero at those angles, making the secant undefined). The range of the secant function is (-∞, -1] U [1, ∞).
Example:
Consider a right triangle where:
- Hypotenuse = 5
- Adjacent = 4
Then, sec(θ) = 5/4 = 1.25
Secant Graph:
The graph of the secant function has vertical asymptotes at angles where cosine is zero. It repeats its pattern every 2π radians.
Key Uses:
- Secant, along with other trigonometric functions, is widely used in calculus, physics, engineering, and navigation.
- It is used in solving problems related to triangles and angles.
