Answer
375.6k+ views
Hint: In this problem, we have to find how \[\sin x=0\] equals \[\pi \]. We should always know that the sine value is always equal to zero for every multiple of \[\pi \], where \[\pi \] radians is equal to \[{{180}^{\circ }}\]. We can now draw a graph with a sine curve to see the value of sine for \[\pi \].
Complete step by step answer:
We know that the given trigonometric function given is sine.
We should always remember that the sine value is always equal to zero for every multiple of \[\pi \], where \[\pi \] radians is equal to \[{{180}^{\circ }}\].
We can now draw a graph with a sine curve to see the value of sine for \[\pi \].
We can now see that the sine curve touches the line at 0 in every multiple of \[\pi \].
We can now write it as,
\[\Rightarrow \sin x=0\to x=k\times \pi \]
Where k is any whole number.
Therefore, we can summarize that every multiple of \[\pi \] for the sine function is always equal to zero.
Note: Students should also remember that \[\pi \] radians is equal to \[{{180}^{\circ }}\]. We should also know that the sine function goes from 0 to \[{{90}^{\circ }}=\dfrac{\pi }{2}\]and then back to 0 to \[{{180}^{\circ }}=\pi \], and when we come down to -1 to \[{{270}^{\circ }}=\dfrac{3\pi }{2}\] and when we go up to 0 again at \[{{360}^{\circ }}=2\pi \], therefore, it will be 0 at every multiple of \[\pi \]. We should also concentrate in the graph part while drawing the sine curve.
Complete step by step answer:
We know that the given trigonometric function given is sine.
We should always remember that the sine value is always equal to zero for every multiple of \[\pi \], where \[\pi \] radians is equal to \[{{180}^{\circ }}\].
We can now draw a graph with a sine curve to see the value of sine for \[\pi \].
![seo images](https://www.vedantu.com/question-sets/e57dac2b-980c-4c2c-b396-4b9febee81f25008884160671426847.png)
We can now see that the sine curve touches the line at 0 in every multiple of \[\pi \].
We can now write it as,
\[\Rightarrow \sin x=0\to x=k\times \pi \]
Where k is any whole number.
Therefore, we can summarize that every multiple of \[\pi \] for the sine function is always equal to zero.
Note: Students should also remember that \[\pi \] radians is equal to \[{{180}^{\circ }}\]. We should also know that the sine function goes from 0 to \[{{90}^{\circ }}=\dfrac{\pi }{2}\]and then back to 0 to \[{{180}^{\circ }}=\pi \], and when we come down to -1 to \[{{270}^{\circ }}=\dfrac{3\pi }{2}\] and when we go up to 0 again at \[{{360}^{\circ }}=2\pi \], therefore, it will be 0 at every multiple of \[\pi \]. We should also concentrate in the graph part while drawing the sine curve.
Recently Updated Pages
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of friction in our daily life
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology 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)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry 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)
10 examples of evaporation in daily life with explanations
![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)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)