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I'm just wondering if anybody can check my solution to the given problem.

The problem is: Find the exact values of $x$ in $[0,750]$ that satisfy the equation $sin(x) = 1.$

My approach:

The equation $sin(x)=1$ is true when $x=\frac{\pi}2 + 2{\pi}n$. The period of $sin(x)$ is $2{\pi}$. Given the interval $[0,750]$, the highest integer solution for $n$ is $119$, since $\frac{750}{2\pi} \approx 119$. The solution is $\{x: x=\frac{\pi}2 + 2{\pi}n\ $(where $n$ is an integer, and $0 \le n \le 119$)}.

Is this correct? and if not, is it the right approach at least? if it is, are there other ways of solving this?

Thanks.

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YOU are right. I cannot find any errors.

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