Answer
$\sin 56^{\circ}40′$ = 0.8355
Work Step by Step
First we will convert $56^{\circ}40′$ to decimal degrees, let's break it as-
$56^{\circ}40′$ = $56^{\circ}$ + $40′$
Now on dividing 40′ by 60, we have the number of "decimal degrees" equivalent to 40′ (as $1^{\circ}$=60′)
Therefore
$56^{\circ}40′$ = $56^{\circ} + (\frac{40}{60})^{\circ}$
$56^{\circ}40′$ = $56^{\circ} + 0.6667^{\circ}$
$56^{\circ}40′$ = $56.6667^{\circ}$
Now
Using calculator in degree mode-
$\sin 56.6667^{\circ}$ = 0.8354881311
Rounding it to four places past the decimal point-
$\sin 56.6667^{\circ}$ = 0.8355
Therefore-
$\sin 56^{\circ}40′$ = 0.8355
