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MATHS 5 Marks Questions

Graphs Of Trigonometric Functions · UP Board (UPMSP) STD 11 Science (UPMSP - English Medium). 19 questions.

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19 questions · self-marked practice — reveal the answer and mark yourself.

Question 15 Marks
Sketch the graphs of the following pairs of functions on the same axes:
$\text{f(x)}=\sin\frac{\text{x}}{2},\text{g(x)}=\sin\text{x}$
Answer
$\text{f(x)}=\sin\frac{\text{x}}{2},\text{g(x)}=\sin\text{x}$ Clearly, $\sin\frac{\text{x}}{2}$ and $\sin\text{x}$ is a periodic function with period $4\pi$ and $2\pi,$ respectively. The graphs of $\text{f(x)}=\sin\frac{\text{x}}{2}$ and $\text{g(x)}=\sin\text{x}$ on different axes are shown below:

If these two graphs are drawn on the same axes, then the graph is shown below.
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Question 25 Marks
Sketch the graphs of the following trigonometric functions:
$\text{u(x)}=\cos^2\frac{\text{x}}{2}$
Answer
$\text{u(x)}=\cos^2\frac{\text{x}}{2}$
$\text{y}=\cos^2\frac{\text{x}}{2}$
The following graph is:
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Question 35 Marks
Sketch the graphs of the following trigonometric functions:
$\text{g(x)}=\cos2\pi\text{x}$
Answer
$\text{g(x)}=\cos2\pi\text{x}$
$\text{y}=\cos2\pi\text{x}$
The following graph is:
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Question 45 Marks
Sketch the graphs of the following functions:
$\text{f(x)}=\sec^2\text{x}$
Answer
$\text{f(x)}=\sec^2\text{x}$
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Question 55 Marks
Sketch the graphs of the following trigonometric functions:
$\text{h(x)}=\cos^22\text{x}$
Answer
$\text{h(x)}=\cos^22\text{x}$ $\text{y}=\cos^22\text{x}$ The following graph is:
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Question 65 Marks
Sketch the graphs of the following functions:
$\text{f(x)}=\cot2\text{x}$
Answer
$\text{f(x)}=\cot2\text{x}$
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Question 75 Marks
Sketch the graphs of the following functions:
$\text{f(x)}=3\sec\text{x}$
Answer
$\text{f(x)}=3\sec\text{x}$
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Question 85 Marks
Sketch the graphs of the following functions:
$\text{f(x)}=\cot^2\text{x}$
Answer
$\text{f(x)}=\cot^2\text{x}$
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Question 95 Marks
Sketch the graphs of the following curves on the same scale and the same axes:
$\text{y}=\cos\text{x}$ and $\text{y}=\cos\frac{\text{x}}{2}$
Answer
First, we draw the graph of $\text{y}=\cos\text{x}.$
Let us now draw the graph of $\text{y}=\cos\Big(\frac{\text{x}}{2}\Big).$
$\Rightarrow\text{y}=\cos\frac{1}{2}(\text{x})$
Then, we will obtain the following graph:
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Question 105 Marks
Sketch the graphs of the following trigonometric functions:
$\text{f(x)}=\cos\pi\text{x}$
Answer
$\text{f(x)}=\cos\pi\text{x}$
$\text{y}=\cos\pi\text{x}$
The following graph is:
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Question 115 Marks
Sketch the graphs of the following functions:
$\text{f(x)}=\cot\frac{\pi\text{x}}{2}$
Answer
$\text{f(x)}=\cot\frac{\pi\text{x}}{2}$
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Question 125 Marks
Sketch the graphs of the following functions:
$\text{f(x)}=\text{cosec}^2\text{x}$
Answer
$\text{f(x)}=\text{cosec}^2\text{x}$
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Question 135 Marks
Sketch the graphs of the following functions:
$\text{f(x)}=\tan^2\text{x}$
Answer
$\text{f(x)}=\tan^2\text{x}$
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Question 145 Marks
Sketch the graphs of the following curves on the same scale and the same axes:
$\text{y}=\cos2\text{x}$ and $\text{y}=\cos2\Big(\text{x}-\frac{\pi}{4}\Big)$
Answer
First, we draw the graph of $\text{y}=\cos2\text{x}.$ Let us now draw the graph of $\text{y}=\cos2\Big(\text{x}-\frac{\pi}{4}\Big).$ $\text{y}=\cos2\Big(\text{x}-\frac{\pi}{4}\Big)$ $\Rightarrow\text{y}-0=\cos2\Big(\text{x}-\frac{\pi}{4}\Big)...(\text{i})$ 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: $\text{Y}=\cos2\text{X}$ Then, we draw the graph of $\text{Y}=\cos2\text{X}$ and shift it by $\frac{\pi}{4}$ to the right. Then, we will obtain the following graph:
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Question 155 Marks
Sketch the graphs of the following functions:
$\text{f(x)}=2\sec\pi\text{x}$
Answer
$\text{f(x)}=2\sec\pi\text{x}$
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Question 165 Marks
Sketch the graphs of the following curves on the same scale and the same axes:
$\text{y}=\cos^2\text{x}$ and $\text{y}=\cos\text{x}$
Answer
First, we draw the graph of $\text{y}=\cos^2\text{x}.$ Let us now draw the graph of $\text{y}=\cos\text{x}.$ Then, we will obtain the following graph:
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Question 175 Marks
Sketch the graphs of the following trigonometric functions:
$\phi\text{(x)}=2\cos\Big(\text{x}-\frac{\pi}{6}\Big)$
Answer
$\phi\text{(x)}=2\cos\Big(\text{x}-\frac{\pi}{6}\Big)$ $\text{y}=2\cos\Big(\text{x}-\frac{\pi}{6}\Big)$ $\Rightarrow\text{y}-0=2\cos\Big(\text{x}-\frac{\pi}{6}\Big)...(\text{i})$ On shifting the origin at $\Big(\frac{\pi}{6},0\Big),$ we get: $\text{x = X}+\frac{\pi}{6}$ and $\text{y = Y}+0$ On subsitituting the values in (i), we get: $\text{Y}=2\cos\text{X}$ Then, we draw the graph of $\text{Y}=\cos\text{X}$ and shift it by $\frac{\pi}{6}$ to the right. Then, we obtain the following graph:
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Question 185 Marks
Sketch the graphs of the following functions:
$\text{f(x)}=\tan2\text{x}$
Answer
$\text{f(x)}=\tan2\text{x}$
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Question 195 Marks
Sketch the graphs of the following functions:
$\text{f(x)}=2\text{cosec }\pi\text{x}$
Answer
$\text{f(x)}=2\text{cosec }\pi\text{x}$
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5 Marks Questions - MATHS STD 11 Science Questions - Vidyadip