Solving Trig Equations with Multiple Angles

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $0=\sin2x$  

•  $x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2}$  

•  $x=0,\pi$  

•  $No\ Solutions$  

•  $x=0,\pi,2\pi,3\pi$  

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $\frac{1}{2}=\sin3x$  

•  $x=\frac{\pi}{18},\frac{5\pi}{18},\frac{13\pi}{18},\frac{17\pi}{18},\frac{25\pi}{18},\frac{29\pi}{18}$  

•  $x=\frac{\pi}{18},\frac{5\pi}{18},\frac{13\pi}{18},\frac{17\pi}{18}$  

•  $x=\frac{\pi}{6},\frac{5\pi}{6},\frac{13\pi}{6},\frac{17\pi}{6},\frac{25\pi}{6},\frac{29\pi}{6}$  

•  $x=\frac{\pi}{6},\frac{5\pi}{6}$  

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $\cos2x=\frac{\sqrt{2}}{2}$  

•  $x=\frac{\pi}{8},\frac{7\pi}{8},\frac{9\pi}{8},\frac{15\pi}{8}$  

•  $x=\frac{\pi}{4},\frac{7\pi}{4},\frac{9\pi}{4},\frac{15\pi}{4}$  

•  $x=\frac{\pi}{4},\frac{7\pi}{4}$  

•  $No\ Solution$  

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $\csc3x=-\frac{2\sqrt{3}}{3}$  

•  $x=\frac{4\pi}{9},\frac{5\pi}{9},\frac{10\pi}{9},\frac{11\pi}{9}$  

•  $x=\frac{4\pi}{9},\frac{5\pi}{9},\frac{10\pi}{9},\frac{11\pi}{9},\frac{16\pi}{9},\frac{17\pi}{9}$  

•  $x=\frac{4\pi}{3},\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3},\frac{16\pi}{3},\frac{17\pi}{3}$  

•  $No\ Solutions$  

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $-\frac{\sqrt{3}}{2}=\cos3x$  

•  $x=\frac{5\pi}{18},\frac{7\pi}{18},\frac{17\pi}{18},\frac{19\pi}{18},\frac{29\pi}{18},\frac{31\pi}{18}$  

•  $x=\frac{5\pi}{6},\frac{7\pi}{6},\frac{17\pi}{6},\frac{19\pi}{6},\frac{29\pi}{6},\frac{31\pi}{6}$  

•  $No\ Solutions$  

•  $x=\frac{5\pi}{6},\frac{7\pi}{6}$  

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $-\frac{\sqrt{3}}{2}=\sin x$  

•  $x=\frac{4\pi}{3},\frac{5\pi}{3}$  

•  $x=\frac{\pi}{3},\frac{2\pi}{3}$  

•  $No\ Solutions$  

•  $x=\frac{\pi}{3},\frac{5\pi}{3}$  

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $\frac{\sqrt{3}}{2}=\cos2x$  

•  $x=\frac{\pi}{12},\frac{11\pi}{12},\frac{13\pi}{12},\frac{23\pi}{12}$  

•  $x=\frac{\pi}{6},\frac{11\pi}{6},\frac{13\pi}{6},\frac{23\pi}{6}$  

•  $No\ Solutions$  

•  $x=\frac{\pi}{6},\frac{11\pi}{6}$  

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $\tan3x=1$  

•  $x=\frac{\pi}{12},\frac{5\pi}{12},\frac{3\pi}{4},\frac{13\pi}{12},\frac{17\pi}{12},\frac{7\pi}{4}$  

•  $x=\frac{\pi}{4},\frac{5\pi}{4},\frac{9\pi}{4},\frac{13\pi}{4},\frac{17\pi}{4},\frac{21\pi}{4}$  

•  $No\ Solutions$  

•  $x=\frac{\pi}{4},\frac{5\pi}{4}$