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

611

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

612

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

613

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

614

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

615  

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

616

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

617

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

618

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

619

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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)

6121

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

6122

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

6123

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

6124