Question

If $\cos 3x=-1$, where $0^o\ge x\ge {360}^o$, then $x$

• A. ${60}^o,{180}^o,{300}^o$
• B. ${180}^o$
• C. ${60}^o,{180}^o$
• D. ${180}^o,{300}^o$

Answer 1

The correct option is A ${60}^o,{180}^o,{300}^o$

Given $\cos 3x=-1$

$⟹3x=2n\pi \pm \pi =(2n\pm 1)\pi$ where $n$ is an integer

$⟹x=\frac{(2n\pm 1)\pi }{3}$

$⟹x=(2n\pm 1){60}^{\circ }=\pm {60}^{\circ },\pm {180}^{\circ },\pm {300}^{\circ },\pm {420}^{\circ },\cdots$

As $0^{\circ }\le x\le {360}^{\circ },x={60}^{\circ },{180}^{\circ },{300}^{\circ }$