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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
B. Trigonometric Functions
18. 12AF.B2.3
18.3 Cosecant graph: y = csc x
Cosecant Graph: y = csc x
See how to graph y = csc x step by step, including its period, vertical asymptotes, domain, range, and worked examples.
What You'll Learn
The cosecant function is the reciprocal of sine, so csc x equals 1 divided by sin x
The cosecant graph has vertical asymptotes wherever sine equals zero, at every multiple of pi
Cosecant has period 2 pi and a range of y less than or equal to negative 1 or y greater than or equal to 1
Sketching the sine curve first makes it easy to place the asymptotes and U-shaped branches of the cosecant graph
Transformations like stretches and shifts move the cosecant graph the same way they move other trig graphs
What You'll Practice
1
Drawing sine graphs first to establish the base function
2
Converting x-intercepts to vertical asymptotes
3
Plotting reciprocal values and invariant points on the coordinate plane
4
Sketching complete cosecant curves by flipping sine wave orientations
Why This Matters
Understanding the cosecant graph deepens your grasp of reciprocal trigonometric functions, which appear throughout precalculus, calculus, and physics. Mastering how to visualize and sketch csc x from sin x builds essential graphing skills you'll use when analyzing wave behavior, oscillations, and periodic phenomena.
This Unit Includes
1 Video lesson
Learning resources
Skills
Cosecant Function
Reciprocal Functions
Trigonometric Graphs
Asymptotes
Invariant Points
Sine Function
Graph Transformations
ON Curriculum Aligned