Overview

Foundations of Mathematics 12 (MAT621A)

Relations and Functions

8. Represent data using sinusoidal functions to solve problems

8.5 Secant graph: y = sec x

Secant Graph: y = sec x

Understand the secant graph y = sec x, including its domain, range, asymptotes, and period, with clear worked examples.

What You'll Learn

The secant function is the reciprocal of cosine, so y = sec x equals 1 divided by cos x.

Vertical asymptotes occur wherever cos x equals zero, which is at x equals pi over 2 plus any multiple of pi.

The range of y = sec x is all values less than or equal to negative 1 or greater than or equal to 1, and it never touches the strip between them.

The secant graph is periodic with period 2 pi and is an even function, so its graph is symmetric about the y-axis.

Changing y = sec x to y = sec(2x) compresses the graph horizontally and shortens the period to pi.

What You'll Practice

Graphing secant functions by finding reciprocals of cosine values

Identifying and drawing vertical asymptotes at x = π/2, 3π/2, etc.

Plotting invariant points and reciprocal coordinates

Sketching U-shaped curves that open opposite to cosine portions

Why This Matters

Understanding the secant graph builds your foundation in trigonometric functions and their relationships. You'll use secant in calculus, physics, and engineering applications involving wave functions, oscillations, and circular motion where reciprocal trig relationships are essential.

Before You Start — Make Sure You Can:

Use sine ratio to calculate angles and sides (Sin = \( \frac{o}{h}\) )Radian measure and arc length Converting between degrees and radians Cosine graph: y = cos x

This Unit Includes

1 Video lesson

Learning resources

Skills

Secant Function

Reciprocal Functions

Trigonometric Graphs

Vertical Asymptotes

Invariant Points

Cosine

Function Transformations

PEI Curriculum Aligned