What is sin((7pi)/4)?

May 1, 2018

$\sin \left(7 \cdot \frac{\pi}{4}\right)$ = $- \frac{\sqrt{2}}{2}$

Explanation:

$\pi$ in general equals to 3.142 in radian form or 180 degrees since $2 \pi$ = 360 degrees.

To solve the eqn, we need to convert the $\pi$ into degrees.

$\sin \left(7 \cdot \frac{\pi}{4}\right)$ = $\sin \left(7 \cdot \frac{180}{4}\right)$
$\sin \left(7 \cdot \frac{180}{4}\right)$ = $\sin \left(\frac{1260}{4}\right)$
$\sin \left(\frac{1260}{4}\right)$ = $\sin \left(315\right)$
$\sin \left(315\right)$ = $- \frac{\sqrt{2}}{2}$

May 1, 2018

$- 0.707$

Explanation:

$\sin \left(\frac{7 \pi}{4}\right)$

$\therefore \frac{7 {\cancel{\pi}}^{1}}{\cancel{4}} ^ 1 \times {\cancel{180}}^{45} / {\cancel{\pi}}^{1} = {315}^{\circ}$

$\therefore \sin {315}^{\circ} = - 0.707106781$

May 1, 2018

$\rightarrow \sin \left(\frac{7 \pi}{4}\right) = - \frac{1}{\sqrt{2}}$

Explanation:

$\rightarrow \sin \left(\frac{7 \pi}{4}\right) = \sin \left(2 \pi - \frac{\pi}{4}\right) = - \sin \left(\frac{\pi}{4}\right) = - \frac{1}{\sqrt{2}}$