Find the slope of the tangent to y=sin(x) at x=(pi )/(4) Select one: a. (sqrt (2))/(2) b. -(sqrt (2))/(2) C. sqrt (2) d. -sqrt (2)

The slope of the tangent line to the function $y = sin(x)$ at a particular point can be found using the derivative of the function. The derivative of $y = sin(x)$ with respect to x is $y' = cos(x)$. This derivative gives us the slope of the tangent line at any point x. To find the slope at $x = \frac{\pi}{4}$, we substitute this value into the derivative:<br /><br />Slope = $y'(\frac{\pi}{4}) = cos(\frac{\pi}{4})$<br /><br />The cosine of $\frac{\pi}{4}$ is known to be $\frac{\sqrt{2}}{2}$. Therefore, the slope of the tangent to $y = sin(x)$ at $x = \frac{\pi}{4}$ is $\frac{\sqrt{2}}{2}$.