# General solutions for cos(1/x)

• Jun 10th 2013, 08:19 AM
zachd77
General solutions for cos(1/x)
This may seem a bit too simple of a question:

Do we write solutions to cos(1/x) = 0 as:

1/x = PI/2 (+/-) n(PI) where n is an integer or

1/x = n(PI) (+/-) PI/2 where n is an integer?

Is one form of the solution better tan the other? If so, which is the better form?

Thanks!
• Jun 10th 2013, 08:37 AM
Plato
Re: General solutions for cos(1/x)
Quote:

Originally Posted by zachd77
Do we write solutions to cos(1/x) = 0 as:

Make the notation simpler. $\displaystyle \cos(\theta)=0\text{ if and only if }\theta=\frac{(2n+1)\pi}{2}$ where $\displaystyle n\in\mathbb{Z}$.

Now $\displaystyle x=~?$
• Jun 10th 2013, 10:55 AM
HallsofIvy
Re: General solutions for cos(1/x)
Quote:

Originally Posted by zachd77
This may seem a bit too simple of a question:

Do we write solutions to cos(1/x) = 0 as:

1/x = PI/2 (+/-) n(PI) where n is an integer or

If n= 4, then pi/2+ 4pi= (9/2)pi and cos((9/2)pi)= 0

Quote:

1/x = n(PI) (+/-) PI/2 where n is an integer?
If n= 4, then 4(pi/2)+ pi= 3pi and cos(3pi)= -1.

Quote:

Is one form of the solution better tan the other? If so, which is the better form?

Thanks!