Subjects trigonometry

Sin Function

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Sin Function


1. Let's start by understanding the sine function $\sin x$. It represents the ratio of the opposite side to the hypotenuse in a right triangle for an angle $x$. 2. The sine of an angle varies between $-1$ and $1$, depending on the value of $x$. 3. The value $\sin x = 1$ happens specifically when $x$ equals $\frac{\pi}{2} + 2k\pi$ for any integer $k$. This means it is at its maximum value at these points. 4. Hence, $\sin x$ does not turn into 1 for all $x$, but only at specific points where the angle corresponds to $90^\circ$ or $\frac{\pi}{2}$ radians, plus full rotations of $2\pi$ radians. 5. If in your expression $\sin x$ is shown as 1, it might be due to the evaluation at such a point or a simplification in a certain context. 6. To confirm, always check the angle value or the domain in which $\sin x$ is evaluated.