Usa the fact that the trigonometric functions are periodic to find the exact value of the given expression. sin(17pi )/(4) sin(17pi )/(4)= square (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the e

To find the exact value of the given expression, we can use the periodicity of the sine function. The sine function has a period of $2\pi$, which means that the value of the sine function repeats every $2\pi$ radians.<br /><br />In this case, we have $\sin\frac{17\pi}{4}$. To simplify this expression, we can find an equivalent angle within the interval $[0, 2\pi)$.<br /><br />To do this, we can subtract multiples of $2\pi$ from $\frac{17\pi}{4}$ until we get an angle within the desired interval.<br /><br />$\frac{17\pi}{4} - 2\pi = \frac{17\pi}{4} - \frac{8\pi}{4} = \frac{9\pi}{4}$<br /><br />$\frac{9\pi}{4} - 2\pi = \frac{9\pi}{4} - \frac{8\pi}{4} = \frac{\pi}{4}$<br /><br />Now, we have $\sin\frac{\pi}{4}$, which is a common angle in the unit circle. The sine of $\frac{\pi}{4}$ is $\frac{\sqrt{2}}{2}$.<br /><br />Therefore, $\sin\frac{17\pi}{4} = \frac{\sqrt{2}}{2}$.<br /><br />So, the exact value of the given expression is $\frac{\sqrt{2}}{2}$.