functions

A function is a mathematical rule that connects two non-empty subsets of the real numbers, typically denoted as \( A \subseteq \mathbb{R} \) and \( B \subseteq \mathbb{R} \).

The first derivative of a function, \( f'(x) \), reveals where the original function \( f(x) \) is increasing, decreasing, or remains monotonic over specific intervals.

A logarithmic function is defined as a function of the form:

\[ y = \log{_a}x \quad \text{with} \quad a \gt 0 \quad a \neq 1 \quad \forall x \in \mathbb{R}^+\]

The sine function \(f(x) = \sin(x) \) assigns to each angle \(x\), expressed in radians, its corresponding sine value

The secant function \(f(x) = \sec(x)\) is defined as the reciprocal of the cosine function. It assigns to each angle \(x\) the value \(1/\cos(x)\).

The cosecant function \(f(x) = \csc(x) \) is defined as the reciprocal of the sine function. It assigns to each angle x (measured in radians) the value \( 1/\sin(x) \).