(Each question 3 marks)

Question 13 Marks

Sketch the graphs of the following pairs of functions on the same axes: $\text{f(x)}=\sin2\text{x},\text{g(x)}=2\sin\text{x}$

Answer

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

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

View full question & answer→

Question 23 Marks

Sketch the graphs of the following trigonometric functions: $\text{f(x)}=\cos\Big(\text{x}-\frac{\pi}{4}\Big)$

Answer

$\text{f(x)}=\cos\Big(\text{x}-\frac{\pi}{4}\Big)$ $\text{y}=\cos\Big(\text{x}-\frac{\pi}{4}\Big)$ $\Rightarrow\text{y}-0=\cos\Big(\text{x}-\frac{\pi}{4}\Big) ...(\text{i})$ On shifting the origin at $\Big(\frac{\pi}{4},0\Big),$ we get: $\text{x = X}+\frac{\pi}{4}$ and $\text{y = Y}+0$ On subsitituting the values in (i) we get: $\text{Y}=\cos\text{X}$ Then, we draw the graph of $\text{Y}=\cos\text{X}$ and shift it by $\frac{\pi}{4}$ to the right. Then, we obtain the following graph:

View full question & answer→

Question 33 Marks

Sketch the graphs of the following function: $\text{f(x)}=2\sin\pi\text{x},0\leq\text{x}\leq2$

Answer

$\text{f(x)}=2\sin\pi\text{x},0\leq\text{x}\leq2$

$\text{x}$	$0$	$1$
$\text{f(x)}=2\sin\pi\text{x}$	$0$	$0$

View full question & answer→

Question 43 Marks

Sketch the graphs of the following trigonometric functions: $\text{g(x)}=\cos\Big(\text{x}+\frac{\pi}{4}\Big)$

Answer

$\text{g(x)}=\cos\Big(\text{x}+\frac{\pi}{4}\Big)$ $\text{y}=\cos\Big(\text{x}+\frac{\pi}{4}\Big)$ $\Rightarrow\text{y}-0=\cos\Big(\text{x}+\frac{\pi}{4}\Big) ...(\text{i})$ On shifting the origin at $\Big(-\frac{\pi}{4},0\Big),$ we get: $\text{x}=\text{X}-\frac{\pi}{4}$ and $\text{y = Y}+0$ On subsitituting the values in (i), we get: $\text{Y}=\cos\text{X}$ Then, we draw the graph of $\text{Y}=\cos\text{X}$ and shift it by $\frac{\pi}{4}$ to the left. Then, we obtain the following graph:

View full question & answer→

Question 53 Marks

Sketch the graphs of the following function: $\text{u(x)}=\sin^2\text{x},0\leq\text{x}\leq2\pi$ $\text{v(x)}=|\sin\text{x}|,0\leq\text{x}\leq2\pi$

Answer

$\text{u(x)}=\sin^2\text{x},0\leq\text{x}\leq2\pi$ $\text{v(x)}=|\sin\text{x}|,0\leq\text{x}\leq2\pi$

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

$\text{x}$	$0$	$\pi$
$\text{v(x)}=\|\sin\text{x}\|$	$0$	$0$

View full question & answer→

Question 63 Marks

Sketch the graphs of the following function: $\text{h(x)}=2\sin3\text{x},0\leq\text{x}\leq\frac{2\pi}{3}$

Answer

$\text{h(x)}=2\sin3\text{x},0\leq\text{x}\leq\frac{2\pi}{3}$

$\text{x}$	$0$	$\frac{\pi}{3}$	$\frac{2\pi}{3}$
$\text{h(x)}=2\sin3\text{x}$	$0$	$0$	$0$

View full question & answer→

Question 73 Marks

Sketch the graphs of the following trigonometric functions: $\psi\text{(x)}=\cos3\text{x}$

Answer

$\psi\text{(x)}=\cos3\text{x}$ $\text{y}=\cos3\text{x}$ The following graph is:

View full question & answer→

Question 83 Marks

Sketch the graphs of the following curves on the same scale and the same axes: $\text{y}=\cos\text{x}$ and $\text{y}=\cos\Big(\text{x}-\frac{\pi}{4}\Big)$

Answer

First, we draw the graph of $\text{y}=\cos\text{x}.$ Let us now draw the graph of $\text{y}=\cos\Big(\text{x}-\frac{\pi}4{}\Big).$ $\text{y}=\cos\Big(\text{x}-\frac{\pi}{4}\Big)$ $\Rightarrow\text{y}-0=\cos\Big(\text{x}-\frac{\pi}{4}\Big)...(\text{i})$ On shifting the origin at $\Big(\frac{\pi}{4},0\Big),$ we get: $\text{x = X}+\frac{\pi}{4}$ and $\text{y = Y}+0$ On subsitituting the values in (i), we get: $\text{Y}=\cos\text{X}$ Then, we draw the graph of $\text{Y}=\cos\text{X}$ and shift it by $\frac{\pi}{4}$ to the right. Then, we will obtain the following graph:

View full question & answer→

MATHS (Each question 3 marks)

Take a timed test