Solving Trigonometric Equations

Solve the equation on the interval $0\le x<2\pi$  

 $2\sin x\ =\ \sqrt{2}$  

•  $\frac{\pi}{4}$  

•  $\frac{\pi}{4},\frac{3\pi}{4}$  

•  $\frac{5\pi}{4},\frac{7\pi}{4}$  

•  $\frac{\pi}{6}$  

Solve the equation on the interval $0\le x<2\pi$  

 $1+\sin x\ =\ 2\cos^2x\$  

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

•  $\frac{\pi}{6},\frac{5\pi}{6}$  

•  $\frac{\pi}{2},\frac{3\pi}{2}$  

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

Solve the equation on the interval $0\le x<2\pi$  

 $x+4\cos x=0$  

•  $2.13,\ 3.60$  

•  $\frac{\pi}{4},\frac{3\pi}{4}$  

•  $\frac{3\pi}{4},\frac{7\pi}{4}$  

•  $3.05,\ 4.76$  

Solve the equation on the interval $0\le x<2\pi$ 
 $\sin^2x-1=0$   

•  $\frac{\pi}{2}$  

•  $\frac{\pi}{2},\frac{3\pi}{2}$  

•  $0,\pi$  

•  $\pi$  

Solve the equation on the interval $0\le x<2\pi$ 

 $4\cos x-\sqrt{3}=2\cos x$   

•  $\frac{\pi}{3},\frac{5\pi}{3}$  

•  $\frac{5\pi}{6},\frac{7\pi}{6}$  

•  $\frac{\pi}{6},\frac{11\pi}{6}$  

•  $\frac{2\pi}{3},\frac{4\pi}{3}$  

Solve the equation on the interval $0\le x<2\pi$ .

 $\sin\frac{x}{2}=-\frac{1}{2}$   

•  $\frac{7\pi}{3},\frac{11\pi}{3},\frac{23\pi}{3},\frac{35\pi}{3}$  

•  $\frac{7\pi}{6},\frac{11\pi}{6}$  

•  $\frac{7\pi}{3},\frac{11\pi}{3}$  

• No solution on the interval

Solve the equation on the interval $0\le x<2\pi$ . 
 $\tan x\cos x+\sin x=-1$  

•  $0.55,\ 2.12$  

•  $1.67,\ 3.55$  

•  $\frac{7\pi}{6},\frac{11\pi}{6}$  

• No solution on the interval

Solve the equation on the interval $0\le x<2\pi$  .
 $4\sin^2x-3=0$  

•  $\frac{\pi}{3}$  

•  $\frac{\pi}{3},\frac{2\pi}{3}$  

•  $\frac{\pi}{3},\ \frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$  

•  $\frac{\pi}{6},\frac{5\pi}{6}$  

Solve the equation on the interval $0\le x<2\pi$ .

 $\sin2x=\cos x$   

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

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

•  $\frac{\pi}{6},\frac{5\pi}{6}$  

• No solution on the interval

Solve the equation on the interval $0\le x<2\pi$ .

 $\sqrt{3}\sec x+2=0$   

•  $\frac{\pi}{6}$  

•  $\frac{2\pi}{3}$  

•  $\frac{2\pi}{3},\frac{4\pi}{3}$  

•  $\frac{5\pi}{6},\frac{7\pi}{6}$