Answer
398.1k+ views
Hint: To graph the given function $y=-\dfrac{1}{2}\cos x$, first of all, we are going to draw the graph of $\cos x$ and then multiply the negative of 1 with $\cos x$. When we multiply the negative of 1 with $\cos x$ then we have to take the mirror image of the graph of $\cos x$ in the line mirror present on the x axis. Now, we will multiply one half to $-\cos x$ then we have to shrink the y value of the graph of $-\cos x$ by one half.
Complete step-by-step answer:
The function given in the above problem which we have to graph is as follows:
$y=-\dfrac{1}{2}\cos x$
To draw the above function on the graph paper, first of all, we are going to draw $\cos x$ on the graph. In the below, we have drawn the graph of $\cos x$.
Now, we are going to draw the graph of $-\cos x$ by taking the mirror image of the above graph in the line mirror placed at x axis.
The dotted line in the above graph is the mirror image of $\cos x$ in the line mirror of x axis so the dotted line pink graph above is of $-\cos x$.
Now, we are drawing the graph of $-\dfrac{1}{2}\cos x$ by shrinking all the y values of the above graph by $\dfrac{1}{2}$.
In the above graph, as you can see that the y value of the blue curve is lesser than that of the dotted pink curve so the blue curve is the graph of $-\dfrac{1}{2}\cos x$.
Now, we are eliminating the pink dotted curve from the above graph then we get,
Hence, we have drawn the graph of $y=-\dfrac{1}{2}\cos x$ which is shown below:
Note: The mistake that could be possible in the drawing of the above graph is that when converting graph from $\cos x$ to $-\cos x$, you will take the mirror image of the graph in the line mirror placed on the y axis because you think that all the y values are changing so line mirror should present on the y axis. But this is the wrong way of conversion from $\cos x$ to $-\cos x$ so make sure you won’t make this mistake in the exam.
Complete step-by-step answer:
The function given in the above problem which we have to graph is as follows:
$y=-\dfrac{1}{2}\cos x$
To draw the above function on the graph paper, first of all, we are going to draw $\cos x$ on the graph. In the below, we have drawn the graph of $\cos x$.
![seo images](https://www.vedantu.com/question-sets/35ccb11c-52a4-4f2c-91c0-ed439dfad1d87363029366125832535.png)
Now, we are going to draw the graph of $-\cos x$ by taking the mirror image of the above graph in the line mirror placed at x axis.
![seo images](https://www.vedantu.com/question-sets/36b33fc9-6983-4c56-ac55-18e79a5963271147331957581894929.png)
The dotted line in the above graph is the mirror image of $\cos x$ in the line mirror of x axis so the dotted line pink graph above is of $-\cos x$.
Now, we are drawing the graph of $-\dfrac{1}{2}\cos x$ by shrinking all the y values of the above graph by $\dfrac{1}{2}$.
![seo images](https://www.vedantu.com/question-sets/2bedc017-b79f-46df-a863-fa49b8e22e897088791648632956864.png)
In the above graph, as you can see that the y value of the blue curve is lesser than that of the dotted pink curve so the blue curve is the graph of $-\dfrac{1}{2}\cos x$.
Now, we are eliminating the pink dotted curve from the above graph then we get,
![seo images](https://www.vedantu.com/question-sets/f4c06938-89fc-44be-807a-242c0d6c45543516781266249007582.png)
Hence, we have drawn the graph of $y=-\dfrac{1}{2}\cos x$ which is shown below:
![seo images](https://www.vedantu.com/question-sets/fdf3993e-45c0-4857-b88e-eae932bec35f1081053880116224264.png)
Note: The mistake that could be possible in the drawing of the above graph is that when converting graph from $\cos x$ to $-\cos x$, you will take the mirror image of the graph in the line mirror placed on the y axis because you think that all the y values are changing so line mirror should present on the y axis. But this is the wrong way of conversion from $\cos x$ to $-\cos x$ so make sure you won’t make this mistake in the exam.
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