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Geometry
43. CC.HSF.IF.C.7
43.10 Tangent graph: y = tan x
Tangent Graph: y = tan x
See how the tangent function repeats, where it breaks apart at vertical asymptotes, and how to sketch y = tan x step by step.
What You'll Learn
The tangent graph repeats every pi radians, which is half the period of sine and cosine
Vertical asymptotes occur wherever cosine equals zero, at x equals pi over 2 plus n times pi
The graph of y equals tan x passes through the origin and every multiple of pi, since tangent is zero there
Unlike sine and cosine, tangent has no maximum or minimum value, its range is all real numbers
Each branch of the tangent curve is increasing, climbing from negative infinity up to positive infinity between consecutive asymptotes
What You'll Practice
1
Finding vertical asymptotes in given intervals
2
Calculating the period of transformed tangent functions
3
Determining period changes from horizontal stretches and compressions
Why This Matters
Understanding the tangent graph prepares you for advanced trigonometry, calculus, and physics applications involving periodic phenomena with asymptotic behavior. Mastering tangent functions is essential for analyzing wave patterns, alternating currents, and optimization problems in STEM fields.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Practice exercises
Learning resources
Skills
Tangent Function
Vertical Asymptotes
Period
Trigonometric Graphs
Function Transformations
OH Curriculum Aligned