above is the graph of and the line over the interval .
Where do the two graphs intersect? Give exact answers in radians, separated by commas.
+26387 bove is the graph of y = sin x and the line y = 1/2 over the interval [0,2 pi]. Where do the two graphs intersect? Give exact answers in rad
$$\small{\text{$
\begin{array}{rcl|rcl}
\sin{(x_1)} &=& \frac12 \qquad &
\qquad \sin{(x_1)} &=& \sin{ (180\ensurement{^{\circ}} -x_2) } =\frac12 \\
&&&\\
x_1 &=& \arcsin{( \frac12 )} \qquad &
\qquad \sin{ (180\ensurement{^{\circ}} - x_2) } &=&\frac12 \\
&&&\\
x_1 &=& 30\ensurement{^{\circ}} \qquad &
\qquad 180\ensurement{^{\circ}} - x_2 &=& \arcsin{( \frac12 )} \\
&&&\\
x_1 &=& \frac{\pi}{6} \qquad &
\qquad x_2 &=& 180\ensurement{^{\circ}}-\arcsin{( \frac12 )} \\
&&&\\
&&\qquad & x_2 &=& 180\ensurement{^{\circ}}-30\ensurement{^{\circ}}\\
&&&\\
&&\qquad & x_2 &=& 150\ensurement{^{\circ}}\\
&&&\\
&&\qquad & x_2 &=& \frac56 \cdot \pi\\
\end{array}
$}}$$
+26387 bove is the graph of y = sin x and the line y = 1/2 over the interval [0,2 pi]. Where do the two graphs intersect? Give exact answers in rad
$$\small{\text{$
\begin{array}{rcl|rcl}
\sin{(x_1)} &=& \frac12 \qquad &
\qquad \sin{(x_1)} &=& \sin{ (180\ensurement{^{\circ}} -x_2) } =\frac12 \\
&&&\\
x_1 &=& \arcsin{( \frac12 )} \qquad &
\qquad \sin{ (180\ensurement{^{\circ}} - x_2) } &=&\frac12 \\
&&&\\
x_1 &=& 30\ensurement{^{\circ}} \qquad &
\qquad 180\ensurement{^{\circ}} - x_2 &=& \arcsin{( \frac12 )} \\
&&&\\
x_1 &=& \frac{\pi}{6} \qquad &
\qquad x_2 &=& 180\ensurement{^{\circ}}-\arcsin{( \frac12 )} \\
&&&\\
&&\qquad & x_2 &=& 180\ensurement{^{\circ}}-30\ensurement{^{\circ}}\\
&&&\\
&&\qquad & x_2 &=& 150\ensurement{^{\circ}}\\
&&&\\
&&\qquad & x_2 &=& \frac56 \cdot \pi\\
\end{array}
$}}$$
