What does (pi/2)+2kpi mean?

1. Apr 14, 2013

PhotonW/mass

Hello I was trying to solve this sample problem, but I really dont get it.
The book says this word by word:

The equation sin3x=1 implies

3x=(pi/2)+2kpi, k an integer.
x= (pi/6)+(2kpi/3), k an integer *Divide each side by 3.

Because x is not restricted to a finite interval, the given equation has an infinite number of solutions. All the solutions are represented by the equation

x= (pi/6)+2kpi/3

Okay it lost me when it told me 3x=(pi/2)+2kpi.
I am really confused. This is not solved like the rest of the trigonometric equations.

2. Apr 14, 2013

sz0

Hi, since the trigonometric functions are periodic there is more than one answer to what 3x can equal to sole your equation.
sin(v) = 1 implies v = pi/2 , but but pi/2 + 2*pi or pi/2 + 4*pi will do as well since it is 2pi-preiodic. k represents any number, that is k = 0,+-1,+-2,+-3 etc.

So therefor v = 3x = pi/2 + k*2pi wich gives x= (pi/6)+(2kpi/3)

if x had been restricted then like for example 0<x<2*pi then only x = pi/6 had been an acceptable answer.

3. Apr 17, 2013

saplingg

Hi,

As the previous poster said, consider the fact that the trig functions are periodic.
The cosine function can be called a "many-to-one" function.

So let's think about the function f(x) = cos(x).

Let me ask you, for what values of x does cos(x) = 1? If you can imagine the graph of the cosine function, or maybe the unit circle, you could tell me: cos(0) = 1.

But also, cos(-4π) = cos(-2π) = cos(2π) = cos(4π) = 1.

Therefore, we can say that solutions of x for the equation, are 2π * k, for some integer k.​

Look at the picture I attached for a view of this.
https://www.physicsforums.com/attachment.php?attachmentid=57974&stc=1&d=1366232397

Now, let's apply the same idea to your original question:

sin(3x) = 1
What values of (3x) does sin(3x) = 1?
Well, an obvious one is 3x = π/2, but also 3x = 5π/2, 9π/2 ...

We can apply the same notation, 3x = π/2 + 2π * k

Hope this helps.

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