AP PreCalculus Flashcards: The Secant, Cosecant, and Cotangent Functions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
Define the secant function, $f(\\theta) = \sec \\theta$.
The secant function is the reciprocal of the cosine function, defined as $\sec \\theta = 1/\\cos \\theta$, where $\\cos \\theta \ne 0$.
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Define the secant function, $f(\\theta) = \sec \\theta$.
The secant function is the reciprocal of the cosine function, defined as $\sec \\theta = 1/\\cos \\theta$, where $\\cos \\theta \ne 0$.
Why is the cosecant function undefined for certain values of $\\theta$?
Since cosecant is the reciprocal of sine ($1/\\sin \\theta$), it is undefined wherever the denominator, $\\sin \\theta$, equals zero.
What is a key characteristic of functions that involve quotients of the sine and cosine functions?
They have vertical asymptotes where the function in the denominator equals zero.
Define the cosecant function, $f(\\theta) = \csc \\theta$.
The cosecant function is the reciprocal of the sine function, defined as $\csc \\theta = 1/\\sin \\theta$, where $\\sin \\theta \ne 0$.
What is the fundamental relationship between the cosecant function and the sine function?
The cosecant function is the reciprocal of the sine function.
Where do the vertical asymptotes of the cosecant function's graph occur?
The vertical asymptotes of the cosecant function occur where its reciprocal function, sine, is equal to zero.
What is the fundamental relationship between the secant function and the cosine function?
The secant function is the reciprocal of the cosine function.
Define the cotangent function, $f(\\theta) = \cot \\theta$.
The cotangent function is the reciprocal of the tangent function, defined as $\cot \\theta = 1/\\tan \\theta$, where $\\tan \\theta \ne 0$.
Why is the secant function undefined for certain values of $\\theta$?
Since secant is the reciprocal of cosine ($1/\\cos \\theta$), it is undefined wherever the denominator, $\\cos \\theta$, equals zero.
What is the range of the secant and cosecant functions?
The range for both the secant and cosecant functions is $(-\\infty, -1] \\cup [1, \\infty)$.
Where do the vertical asymptotes of the secant function's graph occur?
The vertical asymptotes of the secant function occur where its reciprocal function, cosine, is equal to zero.