Question

How do we find the period of a function ? like,

y= sinx / 1+cosx

Answer 1

Find out how long it takes to repeat itself.

Answer 2

and how can find that :S ?

Answer 3

should I have to divide by \[2\] ?

Answer 4

2pi i mean

Answer 5

For this, it will be 2pi because both have periods of 2pi

Answer 6

$$y=\frac{\sin x}{1+\cos x}=\frac{\sin x-\sin x\cos x}{1-\cos^2x}=\frac{\sin x-\sin x\cos x}{\sin^2 x}=\csc x-\cot x$$We know \(\csc x\) has a period of \(2\pi\) and \(\cot x\) a period of \(\pi\) thus our function has a period of \(\max\{\pi,2\pi\}=2\pi\)

Answer 7

Oops, \(\operatorname{lcm}(\pi,2\pi)=2\pi\)

Answer 8

can you tell me what you did in the first step ?

Answer 9

Or you can differentiate both