Can you draw its graph ?-6

Geometry Level 3

$\large \sin(x)=\lfloor x \rfloor$

How many real solutions exist for the above equation?

Check out more problems which can solved easily by sketching their graphs, instead of going algebraically. So, try the set : Can you draw its graph ?

0 2 More than 2. 1

2 solutions

Chew-Seong Cheong
Mar 30, 2015

As suggested I used a graph to solve. Using graphs is my favorite wa cany to solve math problems. The graphs for $\sin{x}$ and $\lfloor x \rfloor$ are as follows:

It can be seen from the graph that there are only $\boxed{2}$ solutions to the equation, when $x=0$ and $x= \frac {\pi}{2}$ .

Nice. I usually prefer degrees to radians, and hence thought that x was in degrees. My answer came out to be $1$ because of that.

Rahul Saha - 6 years, 2 months ago

When doing Calculus, it is more convenient to use radians. Use degree for Trigonometry and Geometry.

Chew-Seong Cheong - 6 years, 2 months ago

Abhinav Raichur
Jun 24, 2015

A solution without graph

given equation $sinx = \lfloor x \rfloor$
The RHS is always an integer and sin(x) takes 3 integer values { -1,0,1} the corresponding floored x are {-2,0,1} ....... only two of them lie in the range of sin(x) hence the answer is 2.

Can you draw its graph ?-6

Check out more problems which can solved easily by sketching their graphs, instead of going algebraically. So, try the set : Can you draw its graph ?

2 solutions

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