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Answer
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$- \dfrac { 1 } { 2 }$
Simplify the expression
$\sin\left( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ \pi } \right)$
$ $ Arrange the terms multiplied by fractions $ $
$\sin\left( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ \pi } } { \color{#FF6800}{ 6 } } } \right)$
$\color{#FF6800}{ \sin\left( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ \pi } } { \color{#FF6800}{ 6 } } } \right) }$
$\sin\left( - \dfrac { 5 \pi } { 6 } \right) $ is $ - \sin\left( \dfrac { 5 \pi } { 6 } \right)$
$\color{#FF6800}{ - } \color{#FF6800}{ \sin\left( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ \pi } } { \color{#FF6800}{ 6 } } } \right) }$
$- \color{#FF6800}{ \sin\left( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ \pi } } { \color{#FF6800}{ 6 } } } \right) }$
$ $ Simplify $ $
$- \color{#FF6800}{ \sin\left( \color{#FF6800}{ \dfrac { \color{#FF6800}{ \pi } } { \color{#FF6800}{ 6 } } } \right) }$
$- \color{#FF6800}{ \sin\left( \color{#FF6800}{ \dfrac { \color{#FF6800}{ \pi } } { \color{#FF6800}{ 6 } } } \right) }$
$\sin(\dfrac{\pi}{6}) $ is $ \dfrac{1}{2}$
$- \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } }$
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