Question

Find the number of solutions of sinx= x/5

Answer 1

Here, let f(x)=sinx and g(x)=  

10

x

​

. Also, we know that −1≤sinx≤1

⇒   −1≤  

10

x

​

   or   −10≤x≤10

Thus, sketch both curves when xϵ[−10,10]

From Fig, f(x)=sinx and g(x)=  

10

x

​

 intersect at seven points. So, the number of solutions is seven.

Answer 2

The number of solutions is three.

Step-by-step explanation:

Here, let f(x)=sinx and g(x)=$\frac{x}{5}$ .Also, we know that −1≤sinx≤1

⇒   −1≤ $\frac{x}{5}$ or   −5 ≤ x ≤ 5

Thus, sketch both curves when xϵ[−5,5]

From Fig, f(x)=sinx and g(x)= $\frac{x}{5}$ intersect at three points. So, the number of solutions is three.

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