Trigonometric Equations with linear transformations

 $Solve\ for\ x:\ \ 4\sin\left(3x\right)=2,\ 0\le x\le2\pi$  

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

•  $\frac{\pi}{18},\frac{5\pi}{18},\frac{25\pi}{18},\frac{29\pi}{18}$  

•  $\frac{\pi}{12},\frac{5\pi}{12},\frac{13\pi}{12},\frac{17\pi}{12},\frac{25\pi}{12},\frac{29\pi}{12}$  

 $Solve\ for\ x:\ \ \ \ \ \cos\frac{x}{3}=\frac{1}{2},\ where\ 0\le x\le2\pi$  

•  $\pi$  

•  $\frac{\pi}{3},\frac{5\pi}{3}$  

•  $\frac{\pi}{3},\frac{5\pi}{3},\frac{7\pi}{3}$  

 $\sin\left(x+60^o\right)=\frac{1}{2},\ \ \ \ \ 0\le x\le360$  

• 30,150,390

• 30,150,420

• 30,150

 $\tan\left(2x\right)=-\sqrt{3},\ where\ 0\le x\le\pi$  

•  $\frac{\pi}{3},\frac{5\pi}{3}$  

•  $\frac{2\pi}{3},\frac{5\pi}{6}$  

•  $\frac{2\pi}{3},\frac{5\pi}{3}$  

•  $\frac{\pi}{3},\frac{5\pi}{6}$  

 $\sin^22x-\frac{3}{4}=0,\ \ 0\le x\le2\pi$  

•  $\frac{\pi}{6},\frac{\pi}{3},\frac{4\pi}{6},\frac{5\pi}{3}\frac{7\pi}{6},\frac{4\pi}{3},\frac{5\pi}{3},\frac{11\pi}{6}$  

•  $\frac{\pi}{6},\frac{\pi}{3},\frac{7\pi}{6},\frac{4\pi}{3}$  

•  $\frac{2\pi}{3},\frac{5\pi}{6},\frac{5\pi}{3},\frac{11\pi}{6}$  

 $GDC:\ 3\tan\left(x+0.2\right)=-2,\ -2\pi\le x\le2\pi$  

•  $-3.93,-0.79,\ 2.35,\ 5.50$  

•  $-4,-1,\ 2,\ 6$  

•  $\ 4.39,1.25,1.89,5.03$  

 $GDC:\ \sin2x=0.61,\ \ -180\le x\le180$  

•  $-161.2,-108.8,18.8,71.2$  

•  $-161,-109,\ 19,\ 71$  

•  $18.8,\ 71.2$  

 $\tan\left(x-\frac{\pi}{6}\right)=\frac{1}{\sqrt{3}},\ 0\le x\le2\pi$  

•  $\frac{\pi}{3},\frac{4\pi}{3}$  

•  $\frac{\pi}{3},\frac{4\pi}{3},\frac{13\pi}{3}$  

•  $\frac{\pi}{3},\frac{5\pi}{3},\frac{14\pi}{3}$