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Overview
Geometry
43. CC.HSF.IF.C.7
43.11 Cotangent graph: y = cot x
Cotangent Graph: y = cot x
See exactly how the cotangent graph behaves: its repeating pattern, vertical asymptotes, and zero points, explained step by step with a plotted example.
What You'll Learn
The cotangent function is defined as cot x equals cos x divided by sin x, or the reciprocal of tan x
The graph of y equals cot x repeats every pi radians, which is the same period as the tangent graph
Vertical asymptotes occur wherever sin x equals zero, that is at x equals n times pi for any integer n
Unlike tangent, the cotangent graph decreases across each branch instead of increasing
The x-intercepts of y equals cot x sit at x equals pi over 2 plus n times pi
The range of cotangent is all real numbers, but the domain excludes every multiple of pi
What You'll Practice
1
Converting tangent graph points to their reciprocal values
2
Identifying and marking vertical asymptotes on cotangent graphs
3
Sketching complete cotangent curves using the X-pattern technique
4
Determining zeros and asymptotes by analyzing reciprocal relationships
Why This Matters
Understanding cotangent graphs strengthens your grasp of reciprocal trigonometric functions, a skill essential for advanced calculus, physics, and engineering. Mastering these transformations helps you visualize function behavior and solve complex trigonometric equations efficiently.
This Unit Includes
1 Video lesson
Learning resources
Skills
Cotangent
Reciprocal Functions
Graphing
Vertical Asymptotes
Trigonometry
Function Transformations
Invariant Points
OH Curriculum Aligned