Exercise 11.1 Solutions - Class 11 Mathematics Unit 11 Trigonometric Functions and their Graphs

Step-by-step solved problems and explanations for Exercise 11.1, Unit 11: Trigonometric Functions and their Graphs.Comprehensive solutions covering Domain, Range, Even & Odd properties, and Periods of Trigonometric Functions for Punjab Board Class 11 (PCTB).

This page provides complete, step-by-step solved solutions for Exercise 11.1 of Unit 11: Trigonometric Functions and their Graphs for Class 11 Mathematics under the Punjab Board (PCTB / PECTAA). All problems on determining domains, ranges, algebraic parity (even and odd functions), and calculating fundamental periods of scaled trigonometric expressions such as sin 3x, tan 4x, and 3 cos(x/5) are thoroughly worked out for HSSC Part 1 board exam preparation.
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Exercise Overview

Exercise 11.1 introduces Unit 11: Trigonometric Functions and their Graphs in Class 11 Mathematics, establishing the functional characteristics, domains, ranges, algebraic parity, and periodic cycles of circular trigonometric functions.

The exercise systematically analyzes the domain and range of all six trigonometric functions: showing why sine and cosine are defined for all real numbers with range [-1, 1], while tangent, cotangent, secant, and cosecant possess vertical asymptotes and restricted domains due to zeros in denominators. It establishes the symmetry classifications-cosine and secant being even (f(-x) = f(x)), and sine, tangent, cosecant, and cotangent being odd (f(-x) = -f(x)). Furthermore, students learn the rigorous algebraic method to compute the fundamental period of general transformed functions f(kx), where the standard 2π or π period is divided by the scaling factor k.

In Punjab Board HSSC Part 1 examinations, Exercise 11.1 questions are frequently featured in Section A objective MCQs and Section B short conceptual questions across Lahore, Rawalpindi, Gujranwala, Faisalabad, Multan, and other BISE boards. Mastering these fundamental definitions is critical for drawing accurate trigonometric graphs and understanding signal analysis in higher physics and engineering.

FAQs

Are these Exercise 11.1 solutions according to the Punjab Board syllabus?
Yes, these solutions strictly follow the official Punjab Curriculum and Textbook Board (PCTB / PECTAA) Class 11 Mathematics syllabus for Unit 11 (Trigonometric Functions and their Graphs) for the 2026-2027 academic session.
What are the key concepts covered in Exercise 11.1 Class 11 Mathematics?
Exercise 11.1 covers the domains and ranges of all six circular trigonometric functions, even and odd parity properties, and calculating the fundamental periods of trigonometric functions.
What are the domains and ranges of the six trigonometric functions?
Sine and cosine have domain ℝ and range [-1, 1]. Tangent and secant exclude odd multiples of π/2. Cotangent and cosecant exclude integer multiples of π. Tangent/cotangent range is ℝ, while secant/cosecant range is (-∞, -1] ∪ [1, ∞).
What are even and odd trigonometric functions?
Cosine and secant are even functions because f(-x) = f(x). Sine, cosecant, tangent, and cotangent are odd functions because f(-x) = -f(x).
What is the definition of the period of a trigonometric function?
The period of a function f(x) is the smallest positive real number p such that f(x + p) = f(x) for all x in its domain.
How do you find the period of sin(kx), cos(kx), or tan(kx)?
For sin(kx), cos(kx), sec(kx), and csc(kx), the period is 2π/|k|. For tan(kx) and cot(kx), the period is π/|k|.
Can students read these Exercise 11.1 solutions online?
Yes, students can read all Exercise 11.1 period calculations and domain-range proofs directly online on MaryamNotes.pk on any web browser without downloading.
Are these Class 11 Exercise 11.1 notes completely free to access?
Yes, all solved notes, period calculations, and study materials on MaryamNotes.pk are 100% free and open to all students and teachers across Pakistan.