Secant Equation – sec(x) Identities & Solutions :: Danielitte

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Equations - Sec

Secant Function (sec)

Understanding the Secant Trigonometric Function

The Secant function is the reciprocal of the cosine function in trigonometry. It is defined as:

Definition:

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

Secant Graph

Key Properties:

Undefined when \( \cos(\theta) = 0 \) (i.e., \( \theta = \frac{\pi}{2}, \frac{3\pi}{2}, \ldots \))
Even function: \( \sec(-\theta) = \sec(\theta) \)
Periodicity: \( \sec(\theta + 2\pi) = \sec(\theta) \)
Range: \( (-\infty, -1] \cup [1, \infty) \)

Applications of Secant:

Used in solving right-angled triangle problems
Appears in calculus and integration involving trigonometric identities
Important in wave motion, optics, and engineering
Applied in architecture for slope and height calculations