# 4 waves $\;x_{1}=4 \sin5t\;, x_{2}= 8 \sin 5t\;, x_{3}=\cos 5t \;and\;x_{4}=4 \cos 5t \;$ interfere and if the final equation can be written in the form of $\;A \sin (5t+\sin^{-1}(\large\frac{B}{c}))\;$ , what is the sum of $\;A+B+C$ ?

$(a)\;31\qquad(b)\;25\qquad(c)\;30\qquad(d)\;26$

The final wave is
$x_{1}+x_{2}+x_{3}+x_{4}=12 \sin 5t+ 5 \cos 5t$
$=13\;(\large\frac{12}{13} \sin 5t+ \large\frac{5}{13} \cos 5t)$
$=13\;\sin(5t+\sin^{-1}(\large\frac{5}{13}))$
$A=13\;,B=5\;,c=13$
$A+B+C=31\;.$
edited Jan 11