Introduction
The best Unit 11, Trigonometric Functions and Their Graphs, solved notes for Class 11 Punjab Boards are now available, with 100 percent of exercises solved using easy, step by step solutions, graphs, diagrams, and the marking scheme, based on the new book from PECTAA, the Punjab Curriculum and Textbook Board. These notes are perfect for the 2027 exams and are built to help students score 90 plus marks.
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What’s Inside Unit 11, From Symmetry to Sketching
Unit 11 shifts the focus from evaluating trig ratios to understanding trig functions as, well, functions, with their own symmetry, domain, range, and shape on a graph.
It opens with testing whether a trigonometric expression is even, odd, or neither, using the rules f(−x) = f(x) for even functions and f(−x) = −f(x) for odd functions, applied to expressions that combine multiple trig functions rather than a single ratio.
From there, the unit moves into graphing the six trigonometric functions, covering the shape, amplitude, and period of sin x, cos x, tan x, and their reciprocal functions, along with how to sketch transformed versions involving shifts, stretches, and reflections.
This leads naturally into domain, range, and periodicity, identifying where each trig function is defined, what values it can output, and the smallest interval after which its graph repeats, including the special restrictions that apply to tan, cot, sec, and csc.
The unit closes by tying these ideas together in graph transformations, describing how changes to a function’s equation, such as a coefficient in front or an angle added inside, shift the amplitude, period, or position of the graph compared to the parent function.
Exercise 11.1, Even, Odd, or Neither Functions, Fully Solved
All questions in Exercise 11.1 are fully solved, covering testing trigonometric expressions for symmetry using the even and odd function rules.
| Question | Expression | Result |
|---|---|---|
| Q1(i) | sin²x | Even |
| Q1(ii) | sin x + cos x | Neither |
| Q1(iii) | sin⁴x + cos⁴x | Even |
| Q1(iv) | tan x + sec x | Neither |
| Q1(v) | 1/csc³x | Odd |
| Q1(vi) | (sin x + sin 3x)/(cos x + cos 3x) | Odd |
| Q1(vii) | 1/(sec x + sec³x) | Even |
The full solved PDF for Exercise 11.1 is available, covering every question and part in complete detail.
Exercise 11.2, Graphs, Domain, Range, and Periodicity of Trigonometric Functions, Fully Solved
Exercise 11.2 is fully solved, covering sketching the six trigonometric functions over their standard intervals, identifying the domain and range of each function, and determining the period of standard and modified trig expressions.
Exercise 11.3, Graph Transformations, Fully Solved
Exercise 11.3 is fully solved, covering how amplitude changes, period changes, phase shifts, and vertical shifts alter the graph of a trigonometric function compared to its parent graph, and sketching the resulting transformed curves.
Bonus Resources
- A Trigonometric Functions and Graphs formula sheet PDF for quick reference.
- The top 30 even, odd, and graph transformation shortcuts for faster problem solving.
- Trigonometric Functions and Graphs video lectures.
Why This Unit Matters for Your Overall Score
Trigonometric Functions and Their Graphs is a unit where a wrong guess on a symmetry question or a mislabeled graph tends to come from rushing rather than not knowing the method, since the even and odd tests in Exercise 11.1 follow a fixed procedure once f(−x) is substituted in correctly.
Getting comfortable with the shape, domain, and range of each parent graph in Exercise 11.2 makes the transformation questions in Exercise 11.3 much easier to visualize, since every transformed graph is really just the parent graph stretched, shifted, or flipped in a predictable way.
This unit also sets up the graphical intuition that carries directly into Limits and Continuity, so time spent sketching accurately here pays off well beyond this one chapter.
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Frequently Asked Questions
Which exercises are covered in these Unit 11 notes?
Exercise 11.1 through Exercise 11.3 are covered in full, along with the Unit 11 Review Exercise, spanning even and odd function tests, graphing with domain, range, and periodicity, and graph transformations.
How do I tell if a trig expression is even, odd, or neither?
Replace x with −x in the expression and simplify. If the result is identical to the original expression, it’s even. If the result is the negative of the original expression, it’s odd. If it matches neither, the function is neither even nor odd.
Conclusion
With Exercise 11.1 through Exercise 11.3 and the Review Exercise fully solved, Class 11 students across all nine Punjab boards have a complete, exam ready resource for mastering Trigonometric Functions and Their Graphs ahead of the 2026 exams. Use these notes alongside the bonus formula sheet, shortcuts, and past papers to build both speed and accuracy for your Mathematics exam.
Best of luck for your Class 11 Mathematics exam!