# Can Sin (1/0) have a finite value?

The expression $\sin(\dfrac{1}{0})$ is equivalent to $\sin(\dfrac{orange}{mango})$, i.e has no meaning.

On the other hand,

$\displaystyle \lim_\limits{x \to 0} \sin(\dfrac{1}{x})$does have a finite value, between $-1$ and $1$.

## 13 Replies to “Can Sin (1/0) have a finite value?”

1. Vaibhav Rastogi says:

Sin(1/0) can be written as sin(1/x) where

X is tending towards 0 or we can write it

Lim x-0(1/x)

It is clear from given function is defined for all values of x except 0 bcz at 0 it's value will be infinity .

So the value of sin(1/0) doesn't exist.

2. Rudresh Pandey says:

no,it can not be.

because the range of sin function lies between -1 to +1.

so for any value of domain, function (sinX) value can not be more then +1 or less then -1.

hope it will make you understand.

thank you.

3. Satya says:

Yes, the value is finite. Explanation – as the value of sine function is always between -1 to +1, it'll not depend on the angel for being infinite. It's not possible to find the exact value but it must be difinite between -1 and +1.

4. Azim Javed says:

First of all sin(1/0) was not possible bcz the maximum value of sin is 1 and minimum is -1.

Sin(1/0) =0

5. Nirbhay Thacker says:

It is just a finite value between 1 and -1. But, one can't tell the exact value. Whatever you put in sine and cosine function……they just lie from -1 to 1.

6. Vaibhav Rastogi says:

Ofcourse it is a finite value indeed but you cannot determine the value. Sin x is always between +-1 .

7. Satya says:

Yes because sin function domain between [1,-1] therefore the value is limited between 1&-1 is finite value

8. Abhishek Singh says:

No,it has infinite values

9. Abhishek Singh says:

Yes, sin(1/0) has a finite value bcoz

Sinx belongs to [-1,1] for every value of x.

Hope it helps!!

Regards!

10. Nirbhay Thacker says:

Yes which is lies between -1 to +1

11. Ritesh Arora says:

answer —— it will be an oscillating number between [-1,1].

12. Ritesh Arora says:

Yes and it lies between -1 and +1, it doesn't matter how large angle gets

13. Abhishek Singh says:

Yep. It’s close to my estimate of your IQ, somewhere between -1 and 1, but not exactly sure what.