Question

Find the value of $\sin {45}^{\circ }{51}^{\prime }$

Answer 1

The relevant part of the sine table is given below.

	$0^{\prime }$	$6^{\prime }$	${12}^{\prime }$	${18}^{\prime }$	${24}^{\prime }$	${30}^{\prime }$	${36}^{\prime }$	${42}^{\prime }$	${48}^{\prime }$	${54}^{\prime }$	Mean Diff.
	${0.0}^{\circ }$	${0.1}^{\circ }$	${0.2}^{\circ }$	${0.3}^{\circ }$	${0.4}^{\circ }$	${0.5}^{\circ }$	${0.6}^{\circ }$	${0.7}^{\circ }$	${0.8}^{\circ }$	${0.9}^{\circ }$	$12345$
${46}^{\circ }$									$0.7290$		$6$

Write ${46}^{\circ }{51}^{\prime }={46}^{\circ }{48}^{\prime }=3^{\prime }$. From the table we have
$\sin {46}^{\circ }{48}^{\prime }=0.7290$
Mean Difference for $3^{\prime }=0.0006$
$\therefore sin{46}^{\circ }{51}^{\prime }=0.7290+0.0006=0.7296$