Class 11, Exercise 6.1, Graphs of Trigonometric Functions

Class 11: Graphs of Trigonometric Functions – Exercise 6.1

Date: November 1, 2019Author: ICSE CBSE ISC Board Mathematics Portal for Students 0 Comments

Question 1: Sketch the graphs of the following functions:

i) $f(x) = 2 \sin x , 0 \leq x \leq \pi$ ii) $f(x) = 3 \sin \Big( x -$ $\frac{\pi}{4}$ $\Big), 0 \leq x \leq$ $\frac{5\pi}{4}$

iii) $f(x) = 2 \sin 3x, 0 \leq x \leq$ $\frac{2\pi}{3}$ iv) $f (x) = 2 \sin \Big( 2x -$ $\frac{\pi}{3}$ $\Big), 0 \leq x \leq$ $\frac{7\pi}{5}$

v) $f(x) = 4 \sin 3 \Big( x -$ $\frac{\pi}{4}$ $\Big), 0 \leq x \leq 2\pi$ vi) $f(x) = \sin \Big($ $\frac{x}{2}$ $-$ $\frac{\pi}{4}$ $\Big), 0 \leq x \leq 4\pi$

vii) $f(x) = \sin^2 x , 0 \leq x \leq 2\pi$ ,

viii) $g(x) = |\sin x |, 0 \leq x \leq 2\pi$

ix) $f(x) = 2 \sin \pi x, 0 \leq x \leq 2$

Answer:

i) $f(x) = 2 \sin x , 0 \leq x \leq \pi$

ii) $f(x) = 3 \sin \Big( x -$ $\frac{\pi}{4}$ $\Big), 0 \leq x \leq$ $\frac{5\pi}{4}$

iii) $f(x) = 2 \sin 3x, 0 \leq x \leq$ $\frac{2\pi}{3}$

iv) $f (x) = 2 \sin \Big( 2x -$ $\frac{\pi}{3}$ $\Big), 0 \leq x \leq$ $\frac{7\pi}{5}$

v) $f(x) = 4 \sin 3 \Big( x -$ $\frac{\pi}{4}$ $\Big), 0 \leq x \leq 2\pi$

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vi) $f(x) = \sin \Big($ $\frac{x}{2}$ $-$ $\frac{\pi}{4}$ $\Big), 0 \leq x \leq 4\pi$

vii) $f(x) = \sin^2 x , 0 \leq x \leq 2\pi$ ,

viii) $g(x) = |\sin x |, 0 \leq x \leq 2\pi$

ix) $f(x) = 2 \sin \pi x, 0 \leq x \leq 2$

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Question 2:

i) $f (x) = \sin x , \ \ g(x) = \sin \Big( x +$ $\frac{\pi}{4}$ $\Big)$ ii) $f (x) = \sin x , \ \ g(x) = \sin 2x$

iii) $f (x) = \sin 2x , \ \ g(x) = 2 \sin x$ iv) $f (x) = \sin$ $\frac{x}{2}$ $, \ \ g(x) = \sin x$

Answer:

i) $f (x) = \sin x$ (Red Line) $g(x) = \sin \Big( x +$ $\frac{\pi}{4}$ $\Big)$ (Blue Line)

ii) $f (x) = \sin x$ (Red Line) $g(x) = \sin 2x$ (Blue Line)

iii) $f (x) = \sin 2x$ (Red Line) $g(x) = 2 \sin x$ (Blue Line)

iv) $f (x) = \sin$ $\frac{x}{2}$ (Red Line) $g(x) = \sin x$ (Blue Line)

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