Question 1: Sketch the graphs of the following functions:

$\displaystyle \text{i) } f(x) = 2 \sin x , 0 \leq x \leq \pi \hspace{1.0cm} \text{ii) } f(x) = 3 \sin \Big( x - \frac{\pi}{4} \Big), 0 \leq x \leq \frac{5\pi}{4}$

$\displaystyle \text{iii) } f(x) = 2 \sin 3x, 0 \leq x \leq \frac{2\pi}{3} \hspace{1.0cm} \text{iv) } f (x) = 2 \sin \Big( 2x - \frac{\pi}{3} \Big), 0 \leq x \leq \frac{7\pi}{5}$

$\displaystyle \text{v) } f(x) = 4 \sin 3 \Big( x - \frac{\pi}{4} \Big), 0 \leq x \leq 2\pi \hspace{0.5cm} \text{vi) } f(x) = \sin \Big( \frac{x}{2} - \frac{\pi}{4} \Big), 0 \leq x \leq 4\pi$

$\displaystyle \text{vii) } f(x) = \sin^2 x , 0 \leq x \leq 2\pi$,

$\displaystyle \text{viii) } g(x) = |\sin x |, 0 \leq x \leq 2\pi$

$\displaystyle \text{ix) } f(x) = 2 \sin \pi x, 0 \leq x \leq 2$

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

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

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

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

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

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

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:

$\displaystyle \text{i) } f (x) = \sin x , \ \ g(x) = \sin \Big( x + \frac{\pi}{4} \Big) \hspace{1.0cm} \text{ii) } f (x) = \sin x , \ \ g(x) = \sin 2x$

$\displaystyle \text{iii) } f (x) = \sin 2x , \ \ g(x) = 2 \sin x \hspace{1.0cm} \text{iv) } f (x) = \sin \frac{x}{2} , \ \ g(x) = \sin x$

$\displaystyle \text{i) } f (x) = \sin x \text{ (Red Line) } g(x) = \sin \Big( x + \frac{\pi}{4} \Big) \text{ (Blue Line) }$
$\displaystyle \text{ii) } f (x) = \sin x \text{ (Red Line) } g(x) = \sin 2x \text{ (Blue Line) }$
$\displaystyle \text{iii) } f (x) = \sin 2x \text{ (Red Line) } g(x) = 2 \sin x \text{ (Blue Line) }$
$\displaystyle \text{iv) } f (x) = \sin \frac{x}{2} \text{ (Red Line) } g(x) = \sin x \text{ (Blue Line) }$