Secant-cubed function

This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.
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For functions involving angles (trigonometric functions, inverse trigonometric functions, etc.) we follow the convention that all angles are measured in radians. Thus, for instance, the angle of

$90{}^{\circ }$

is measured as

$\pi /2$

.

Definition

The function, denoted ${\sec }^3$, is defined as the composite of the cube function and the secant function (which in turn is the composite of the reciprocal function and the cosine function). Explicitly, it is given as:

$x\mapsto (\sec x{)}^3=\frac{1}{(\cos x{)}^3}$