(Each question 2 marks)

Question 12 Marks

Sketch the graphs of the following function: $\text{g(x)}=3\sin\Big(\text{x}-\frac{\pi}{4}\Big),0\leq\text{x}\leq\frac{5\pi}{4}$

Answer

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

$\text{x}$	$\frac{\pi}{4}$	$\frac{5\pi}{4}$
$\text{g(x)}=3\sin\Big(\text{x}-\frac{\pi}{4}\Big)$	$0$	$0$

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Question 22 Marks

Sketch the graphs of the following pairs of functions on the same axes: $\text{f(x)}=\sin\text{x},\text{g(x)}=\sin\Big(\text{x}+\frac{\pi}{4}\Big)$

Answer

$\text{f(x)}=\sin\text{x},\text{g(x)}=\sin\Big(\text{x}+\frac{\pi}{4}\Big)$ Clearly, $\sin\text{x}$ and $\sin\Big(\text{x}+\frac{\pi}{4}\Big)$ is a periodic function with period $2\pi.$ The graphs of $\text{f(x)}=\sin\text{x}$ and $\text{g(x)}=\sin\Big(\text{x}+\frac{\pi}{4}\Big)$ on different axes are shown below:

If these two graphs are drawn on the same axes, then the graph is shown below.

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Question 32 Marks

Sketch the graphs of the following pairs of functions on the same axes: $\text{f(x)}=\sin\text{x},\text{g(x)}=\sin2\text{x}$

Answer

$\text{f(x)}=\sin\text{x},\text{g(x)}=\sin2\text{x}$ Clearly, $\sin\text{x}$ and $\sin2\text{x}$ is a periodic function with period $2\pi$ and $\pi,$ respectively. The graphs of $\text{f(x)}=\sin\text{x}$ and $\text{g(x)}=\sin2\text{x}$ on different axes are shown below:

If these two graphs are drawn on the same axes, then the graph is shown below.

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Question 42 Marks

Sketch the graphs of the following function: $\phi\text{(x)}=2\sin\Big(2\text{x}-\frac{\pi}{3}\Big),0\leq\text{x}\leq\frac{7\pi}{5}$

Answer

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

$\text{x}$	$\frac{\pi}{6}$	$\frac{4\pi}{6}$
$\phi\text{(x)}=2\sin\Big(2\text{x}-\frac{\pi}{3}\Big)$	$0$	$0$

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Question 52 Marks

Sketch the graphs of the following function: $\psi\text{(x)}=4\sin3\Big(\text{x}-\frac{\pi}{4}\Big),0\leq\text{x}\leq2\pi$

Answer

$\psi\text{(x)}=4\sin3\Big(\text{x}-\frac{\pi}{4}\Big),0\leq\text{x}\leq2\pi$

$\text{x}$	$\frac{\pi}{4}$	$\frac{7\pi}{12}$
$\psi\text{(x)}=4\sin3\Big(\text{x}-\frac{\pi}{4}\Big)$	$0$	$0$

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Question 62 Marks

Sketch the graphs of the following function: $\text{f(x)}=2\sin\text{x},0\leq\text{x}\leq\pi$

Answer

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

$\text{x}$	$0$	$\pi$
$\text{f(x)}=2\sin\text{x}$	$0$	$0$

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Question 72 Marks

Sketch the graphs of the following function: $\theta\text{(x)}=\sin\Big(\frac{\pi}{2}-\frac{\pi}{4}\Big),0\leq\text{x}\leq4\pi$

Answer

$\theta\text{(x)}=\sin\Big(\frac{\pi}{2}-\frac{\pi}{4}\Big),0\leq\text{x}\leq4\pi$

$\text{x}$	$\frac{\pi}{2}$	$\frac{5\pi}{2}$
$\theta\text{(x)}=\sin\Big(\frac{\pi}{2}-\frac{\pi}{4}\Big)$	$0$	$0$

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MATHS (Each question 2 marks)

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