Find the range of [1/sin{x}] [.] denotes GIF, {.} denotes fractional part.


Find the range of [1/sin{x}]

[.] denotes GIF, {.} denotes fractional part.

Grade:12th Pass

3 Answers

Chetan Mandayam Nayakar
312 Points
11 years ago

Dear Speed,


0≤sin{x}<sin(1 radian)

1/(sin(1 radian))<1/sin{x}<∞

f(x) is any integer greater than [1/sin(1 radian)]

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Ashwin Muralidharan IIT Madras
290 Points
11 years ago

Hi Speed Racer,


Clearly 0≤{x}<1.

So 0≤sin{x}<sin1

Now 1<pie/2, but 1>pie/6.

So sin1<1. but sin1>1/2


So sin{x} can take all values from (0,1/2+delta]...... (where delta is >0)


And hence the range of this function would be all positive integers.

As sin{x} can be = 1/n where n=2,3,4,...... (also sin{x} = 1/2+delta, would give 1/sin{x} lies between 1 to 2)

So [1/sin{x}] = 1.


And hence range is all positive integers.


Hope that helps.


All the best.


Ashwin (IIT Madras).

Shraddha sharma
15 Points
5 years ago
I'm a 12th class student....I'm not good in functions...but .. According to me....  Sin{x} can never be zero...
So. Sin( x- [x] )  also never be zero.... Zero can be written as sin(0) ... Therefore  x-[x] not equal to x should not be equal to [x]... And that's only possible in integral points.... But as I have recommended this site I came to know that its ans. Is  all +ve integers.... And even after going through the solution... I'm not getting the reason that why my way is wrong??? Can anyone please explain this to me????

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