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

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

Dear Speed,

f(x)=[1/sin{x}],0≤{x}<1,

0≤sin{x}<sin(1 radian)

1/(sin(1 radian))<1/sin{x}<∞

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

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We
are all IITians and here to help you in your IIT JEE preparation.

All the best Speed!!!

Regards,

Askiitians Experts

CHETAN MANDAYAM NAYAKAR

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.

Regards,

Ashwin (IIT Madras).