Question

Find the general solutions of each of the following equations :
(1) $\sin x=\frac{\sqrt{3}}{2}$
(2) $\sec x=\sqrt{3}$
(3) $\cot 4x=-1$

Answer 1

(i) $sinx=\frac{\sqrt{3}}{2}$

$\Rightarrow sinx=sin\pi /3$

$\Rightarrow x=n\pi +{(-1)}^n\pi /3$

(ii) $secx=\sqrt{3}$

$\Rightarrow secx={\sec }^{-1}\left({54.7356}^0\right)$

$\therefore$ $x=2n\pi \pm \left({54.7356}^0\right)$

(iii) $\cot 4x=-1$

$\Rightarrow \cot 4x=cot(-\pi /4)\Rightarrow 4x=n\pi +(-\pi /4)$

$\therefore$ $x=\frac{n\pi }{4}-\frac{\pi }{16}$