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Overview
Geometry
43. CC.HSF.IF.C.7
43.12 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
1
Graphing secant functions by finding reciprocals of cosine values
2
Identifying and drawing vertical asymptotes at x = π/2, 3π/2, etc.
3
Plotting invariant points and reciprocal coordinates
4
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.
This Unit Includes
1 Video lesson
Learning resources
Skills
Secant Function
Reciprocal Functions
Trigonometric Graphs
Vertical Asymptotes
Invariant Points
Cosine
Function Transformations
OH Curriculum Aligned