Floors + Trig

Geometry Level pending

⌊ cos ⁡ x ⌋ − ⌈ sin ⁡ x ⌉ + ⌊ tan ⁡ x ⌋ = sin ⁡ x \large \left\lfloor \cos { x } \right\rfloor -\left\lceil \sin { x } \right\rceil +\left\lfloor \tan { x } \right\rfloor =\sin { x }

find the number of solutions to the above equation


The answer is 0.

Hamza A by Hamza A , 19, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

As the LHS is an integer, so is the RHS, that is, sin ⁡ x \sin x . So, either sin ⁡ x = − 1 , 0 , 1 \sin x=-1,0,1 . Checking these cases with cos ⁡ x = − 1 , + 1 \cos x=-1,+1 when sin ⁡ x = 0 \sin x=0 and omitting ∣ sin ⁡ x ∣ = 1 |\sin x|=1 (as then tan ⁡ x \tan x is not defined), we find that these are not the solutions. Hence, no solutions exist.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...