Exercise 11.2 Solutions - Class 11 Mathematics Unit 11 Trigonometric Functions and their Graphs

Step-by-step solved problems, value tables, and graph sketches for Exercise 11.2, Unit 11: Trigonometric Functions and their Graphs.Comprehensive solutions covering Graphs of y = sin x, y = cos x, and y = tan x for Punjab Board Class 11 (PCTB).

This page provides complete, step-by-step solved solutions for Exercise 11.2 of Unit 11: Trigonometric Functions and their Graphs for Class 11 Mathematics under the Punjab Board (PCTB / PECTAA). All problems on tabulating coordinate values, setting up Cartesian scales, plotting continuous sinusoidal waveforms for y = sin x and y = cos x over [-2π, 2π], and graphing asymptotic tangent curves for y = tan x over [-π, π] are thoroughly solved for HSSC Part 1 exam success.
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Exercise Overview

Exercise 11.2 focuses on the geometric and visual representation of trigonometric functions in Unit 11: Trigonometric Functions and their Graphs in Class 11 Mathematics, translating algebraic definitions into precise Cartesian curves.

The exercise systematically guides students through the step-by-step graph construction process: selecting suitable step increments (such as π/6 or 30°), tabulating decimal approximations for function outputs, choosing proportional scale units along the x-axis (radians) and y-axis (real values), and plotting continuous smooth curves for y = sin x and y = cos x across the domain [-2π, 2π]. Additionally, it addresses the discontinuous structure of y = tan x over [-π, π], illustrating how the branches pass through origin inflection points and approach vertical asymptotes at x = ±π/2.

In Punjab Board HSSC Part 1 examinations, graph plotting from Exercise 11.2 is a regular staple in Section C long questions across Lahore, Rawalpindi, Gujranwala, Faisalabad, Multan, and other BISE boards. Mastering these table calculations and graph sketching techniques establishes strong geometric intuition for harmonic motion, alternating current analysis, and wave physics.

FAQs

Are these Exercise 11.2 solutions according to the Punjab Board syllabus?
Yes, these solutions strictly adhere to 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 11.2 Class 11 Mathematics?
Exercise 11.2 covers calculating coordinate value tables, plotting graphs of y = sin x and y = cos x over [-2π, 2π], and plotting y = tan x over [-π, π] showing asymptotic behavior.
How do you construct a table of values to plot y = sin x from -2π to 2π?
Divide the interval [-2π, 2π] into convenient angular steps of π/6 (30°) or π/4 (45°), compute corresponding y values (bounded in [-1, 1]), and plot smooth sinusoidal waves passing through the origin.
What are the key geometric features of the cosine graph y = cos x?
The cosine curve is continuous and smooth with amplitude 1, y-intercept (0, 1), x-intercepts at odd multiples of π/2, local minima at ±π, and a fundamental period of 2π.
How does the tangent curve y = tan x behave near vertical asymptotes?
The tangent curve is discontinuous at odd multiples of π/2 (such as ±π/2), where the function values diverge to +∞ from the left and -∞ from the right, forming repeating branches every π radians.
Can students read these Exercise 11.2 solutions and graph tables online?
Yes, students can view all graph plotting tables, step-by-step coordinates, and curve sketches directly online on MaryamNotes.pk without downloading external files.
Are trigonometric graph plotting questions tested in Punjab Board exams?
Yes, drawing trigonometric graphs with appropriate scale and coordinate tables is a regular long question in Section C across all BISE Punjab boards.
Are these Class 11 Exercise 11.2 notes completely free?
Yes, all solved exercise notes, graphing tables, and educational resources on MaryamNotes.pk are 100% free and open to all students and educators.