Answer
384.3k+ views
Hint: In this problem, we have to graph the given trigonometric equation. We can use a trigonometric identity and we can simplify the given trigonometric expression to get its simplest form. Then we will get an equation for which we can plot the graph by assuming some values.
Complete step by step solution:
We know that the given trigonometric equation is,
\[y=\sin \left( x+\dfrac{\pi }{2} \right)\]
We know that the trigonometric identity can be used in this problem is,
\[\sin \left( a+b \right)=\sin a\cos b+\cos a\sin b\]
We can now compare the above identity and the given trigonometric equation, we get
a = x, b = \[\dfrac{\pi }{2}\]
we can substitute these values in the trigonometric identity, we get
\[\Rightarrow y=\sin x\cos \left( \dfrac{\pi }{2} \right)+\cos x\sin \left( \dfrac{\pi }{2} \right)\]
Now we can substitute the trigonometric degree values in the above step for,
\[\begin{align}
& \cos \dfrac{\pi }{2}=0 \\
& \sin \dfrac{\pi }{2}=1 \\
\end{align}\]
we can substitute the above degree values, we get
\[\begin{align}
& \Rightarrow y=\sin x\times 0+\cos x\times 1 \\
& \Rightarrow y=\cos x \\
\end{align}\]
We can now find the x and y-intercept to plot the points
We know that at y-intercept the value of x is zero.
We can substitute x = 0, we get
\[\Rightarrow y=\cos \left( 0 \right)\]
We know that cos 0 = 1.
Therefore, the y-intercept is \[\left( 0,1 \right)\].
We know that at x-intercept the value of y is zero.
We can substitute y = 0, we get
\[\Rightarrow 0=\cos x\]
We know that when x = \[\pm \dfrac{\pi }{2}\], then the value of y becomes 0.
Therefore, the x-intercepts are \[\left( \dfrac{\pi }{2},0 \right)\left( -\dfrac{\pi }{2},0 \right)\].
Now we can plot the graph
Note: Students make mistakes while finding the correct degree values, which should be concentrated. We should know some trigonometric identities, formula, properties and degree values to solve these types of problems.
Complete step by step solution:
We know that the given trigonometric equation is,
\[y=\sin \left( x+\dfrac{\pi }{2} \right)\]
We know that the trigonometric identity can be used in this problem is,
\[\sin \left( a+b \right)=\sin a\cos b+\cos a\sin b\]
We can now compare the above identity and the given trigonometric equation, we get
a = x, b = \[\dfrac{\pi }{2}\]
we can substitute these values in the trigonometric identity, we get
\[\Rightarrow y=\sin x\cos \left( \dfrac{\pi }{2} \right)+\cos x\sin \left( \dfrac{\pi }{2} \right)\]
Now we can substitute the trigonometric degree values in the above step for,
\[\begin{align}
& \cos \dfrac{\pi }{2}=0 \\
& \sin \dfrac{\pi }{2}=1 \\
\end{align}\]
we can substitute the above degree values, we get
\[\begin{align}
& \Rightarrow y=\sin x\times 0+\cos x\times 1 \\
& \Rightarrow y=\cos x \\
\end{align}\]
We can now find the x and y-intercept to plot the points
We know that at y-intercept the value of x is zero.
We can substitute x = 0, we get
\[\Rightarrow y=\cos \left( 0 \right)\]
We know that cos 0 = 1.
Therefore, the y-intercept is \[\left( 0,1 \right)\].
We know that at x-intercept the value of y is zero.
We can substitute y = 0, we get
\[\Rightarrow 0=\cos x\]
We know that when x = \[\pm \dfrac{\pi }{2}\], then the value of y becomes 0.
Therefore, the x-intercepts are \[\left( \dfrac{\pi }{2},0 \right)\left( -\dfrac{\pi }{2},0 \right)\].
Now we can plot the graph
![seo images](https://www.vedantu.com/question-sets/e33c39ca-c58f-4cc0-aaa7-fd2cb850198f9019180849830568696.png)
Note: Students make mistakes while finding the correct degree values, which should be concentrated. We should know some trigonometric identities, formula, properties and degree values to solve these types of problems.
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)