The number of solutions of the equation x/100=sinx

A) 63

B)32

C) 33

D) 0

Open in App

Solution

Since |sin x|<=1, then x<=100.

We partition the interval [0,100] into segments (0,2pi], (2pi,4pi], ..., (28pi,30pi], (30pi,100]. It is easy to see that there are two solutions in each interval except for (0,2pi] in which there is one solution, in total there are 31 positive solutions. So there must be 31 negative solutions. Since x=0 is also a solution, there are 31+31+1=63 solutions.

Suggest Corrections

Similar questions

x \in [0, 100 π]

{sin}^{4} x - {cos}^{2} x sin x + 2 {sin}^{2} x + sin x = 0

s i n^{100} x - c o s^{100} x = 1

x ε [0, 2 π],

10^{x}

\frac{x}{100} = sin x

Join BYJU'S Learning Program