Answer
385.5k+ views
Hint: For graphing the function which is given in the question as $y=3-\cos x$, we first have to draw the graph of the function $y=\cos x$. Then, we have to obtain the graph of the $y=-\cos x$ from the graph of $y=\cos x$ by taking the reflection of the graph of $y=\cos x$ with respect to the x axis. Finally, the graph of the function $y=3-\cos x$ will be obtained from the graph of the function $y=3-\cos x$ by shifting its graph by three units in the vertical direction.
Complete step by step answer:
From the equation given in the question, we have
$y=3-\cos x......(i)$
We can see that it is related to the basic cosine function, which is given by
$y=\cos x.......(ii)$
The graph corresponding to the above equation is, as we know drawn as
But as we can see in equation (i) that it has negative of $\cos x$. So we have to obtain the graph of
\[\Rightarrow y=-\cos x.......(ii)\]
By comparing equations (ii) and (iii) we can see that the only change is the negative of the dependent variable $y$. So its graph will be obtained by taking the reflection of the above graph with respect to the x-axis, as shown below
Considering the given equation
\[\begin{align}
& \Rightarrow y=3-\cos x \\
& \Rightarrow \left( y-3 \right)=-\cos x.......(iii) \\
\end{align}\]
By comparing (ii) and (iii) we see that the only change is that $3$ in subtracted from the dependent variable $y$. So we need to shift the above graph by $3$ units vertically to obtain the final graph as
Hence, we have drawn the graph of $y=3-\cos x$
Note: Do not do the shifting of the graph before inverting it. Always remember that the shifting of the dependent variable is always done after scaling or inverting it. Also, we must not be confused regarding the direction of shifting. We might argue that as the sign of $3$ in $\left( y-3 \right)$ is negative, the graph must be shifted in the downward direction. But it must be remembered as a key point that the shifting is always done in the opposite direction.
Complete step by step answer:
From the equation given in the question, we have
$y=3-\cos x......(i)$
We can see that it is related to the basic cosine function, which is given by
$y=\cos x.......(ii)$
The graph corresponding to the above equation is, as we know drawn as
![seo images](https://www.vedantu.com/question-sets/99fd2c46-48a3-496c-b58e-0a2aad07c9ba701714656762570307.png)
But as we can see in equation (i) that it has negative of $\cos x$. So we have to obtain the graph of
\[\Rightarrow y=-\cos x.......(ii)\]
By comparing equations (ii) and (iii) we can see that the only change is the negative of the dependent variable $y$. So its graph will be obtained by taking the reflection of the above graph with respect to the x-axis, as shown below
![seo images](https://www.vedantu.com/question-sets/01422a6b-e225-4e24-ac04-7a309c059c044297867237632830961.png)
Considering the given equation
\[\begin{align}
& \Rightarrow y=3-\cos x \\
& \Rightarrow \left( y-3 \right)=-\cos x.......(iii) \\
\end{align}\]
By comparing (ii) and (iii) we see that the only change is that $3$ in subtracted from the dependent variable $y$. So we need to shift the above graph by $3$ units vertically to obtain the final graph as
![seo images](https://www.vedantu.com/question-sets/4003b8ff-bcf0-4f6a-89f0-255d43fe65274839075363000526905.png)
Hence, we have drawn the graph of $y=3-\cos x$
Note: Do not do the shifting of the graph before inverting it. Always remember that the shifting of the dependent variable is always done after scaling or inverting it. Also, we must not be confused regarding the direction of shifting. We might argue that as the sign of $3$ in $\left( y-3 \right)$ is negative, the graph must be shifted in the downward direction. But it must be remembered as a key point that the shifting is always done in the opposite direction.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)