Answer
a) $E=5 \sin (2 \theta+0.927)$
b) $5 \cos 2 \theta -0.644$
Work Step by Step
a) $a \sin B \theta+b \cos B \theta=\sqrt {a^2+b^2} \sin (B \theta+C)$
Now, $E=3 \sin 2 \theta+4 \cos \theta =\sqrt {3^2+4^2} \sin (2 \theta+C)$
or, $=5 \sin (2 \theta+C)$
Now, $C=arctan \dfrac{b}{a} =\tan^{-1} \dfrac{4}{3} \approx 0.927$
and $E=5 \sin (2 \theta+C)=5 \sin (2 \theta+0.927)$
b) $\sqrt {3^2+ 4^2} \cos 2 \theta -arctan \dfrac{3}{4}= 5 \cos 2 \theta -0.644$
