Solving trig equations with multiple angles

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $0=\sin2x$  

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

•  $x=0,\pi$  

•  $No\ Solutions$  

•  $x=0,\pi,2\pi,3\pi$  

Tags

CCSS.HSF.TF.B.7

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $\frac{1}{2}=\sin3x$  

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

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

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

•  $x=\frac{\pi}{6},\frac{5\pi}{6}$  

Tags

CCSS.HSF.TF.B.7

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $\cos2x=\frac{\sqrt{2}}{2}$  

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

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

•  $x=\frac{\pi}{4},\frac{7\pi}{4}$  

•  $No\ Solution$  

Tags

CCSS.HSF.TF.B.7

Solve for ALL answers such that

 $0\le x<2\pi$ :

 $\tan3x=1$  

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

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

•  $No\ Solutions$  

•  $x=\frac{\pi}{4},\frac{5\pi}{4}$  

Tags

CCSS.HSF.TF.B.7

Solve

 $3\tan\ \frac{x}{2}-\sqrt{3}=0$  

•  $\frac{\pi}{3}$  

•  $\frac{\pi}{6},\ \frac{7\pi}{6}$  

•  $\frac{2\pi}{3},\ \frac{5\pi}{3}$  

•  $\frac{4\pi}{3}$