Question

Number of ordered pair $(x,y)$ which satisfy $\left[y\right]=\left[sinx\right]$ ([.] denotes the greatest integer function) and $y=\cos x\forall x\epsilon [0,\frac{\pi }{2}]$ is

• A. 2
• B. 4
• C. infinitely many
• D. none of these

Answer 1

The correct option is C infinitely many

Given

$y=\cos x$

$\left[y\right]=\left[\sin x\right]$

$\left[\cos x\right]=\left[\sin x\right]$

$\left[\cos x\right]$ at $x\in [0,\frac{\pi }{2}]$ is $0$

$\left[\sin x\right]$ at $x\in [0,\frac{\pi }{2}]$ is $0$

Since there are many Points between $0$ and $\frac{\pi }{2}$

Answer is Infinitely Many