Find the exact value of the expression using the provided information.
-Find $\sin ( s - t )$ given that $\cos s = \frac { 1 } { 3 }$, with $s$ in quadrant $I$, and $\sin t = - \frac { 1 } { 2 }$, with $t$ in quadrant IV.
A) $\frac { 2 \sqrt { 6 } - 1 } { 6 }$
B) $\frac { \sqrt { 3 } - 2 \sqrt { 2 } } { 6 }$
C) $\frac { 2 \sqrt { 6 } + 1 } { 6 }$
D) $\frac { \sqrt { 3 } + 2 \sqrt { 2 } } { 6 }$

Question

Quizplus · Accepted Answer

Using the identities $\sin^2 s + \cos^2 s = 1$ and $\sin^2 t + \cos^2 t = 1$, we find $\sin s = \frac{2\sqrt{2}}{3}$ and $\cos t = \frac{\sqrt{3}}{2}$. Then, $\sin(s-t) = \sin s \cos t - \cos s \sin t = \frac{2\sqrt{2}}{3} \cdot \frac{\sqrt{3}}{2} - \frac{1}{3} \cdot \left(-\frac{1}{2}\right) = \frac{2\sqrt{6} + 1}{6}$.

Find the Exact Value of the Expression Using the Provided sin⁡(s−t)\sin ( s - t )sin(s−t)

Find the Exact Value of the Expression Using the Provided $\sin ( s - t )$