Solving Trigonometric Equations - Exact Value

Solve the trigonometric equation below, exact answers only, for

 $0\le x<2\pi$  (This means RADIANS):

 $-1=\cot x$  

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

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

•  $x=\frac{\pi}{6},\frac{7\pi}{6}$  

•  $x=\frac{3\pi}{4},\frac{7\pi}{4}$  

Solve the trigonometric equation below, exact answers only, for

 $0\le x<2\pi$  (This means RADIANS):

 $\tan x=-\frac{\sqrt{3}}{3}$  

•  $x=\frac{\pi}{3}$  

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

•  $x=\frac{5\pi}{6},\frac{11\pi}{6}$  

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

Solve the trigonometric equation below, exact answers only, for

 $0\le x<2\pi$  (This means RADIANS):

 $\csc x=-\sqrt{2}$  

•  $x=\frac{\pi}{6},\frac{5\pi}{4},\frac{7\pi}{6}$  

•  $x=\frac{5\pi}{6},\frac{7\pi}{4}$  

•  $No\ Solution$  

•  $x=\frac{5\pi}{4},\frac{7\pi}{4}$  

Solve the trigonometric equation below, exact answers only, for

 $0\le x<2\pi$  (This means RADIANS):

 $\tan x=-\sqrt{3}$  

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

•  $x=\frac{11\pi}{6}$  

•  $x=\frac{5\pi}{6},\frac{11\pi}{6}$  

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

Solve the trigonometric equation below, exact answers only, for

 $0\le x<2\pi$  (This means RADIANS):

 $\cos x=\frac{1}{2}$  

•  $x=\frac{\pi}{3},\frac{5\pi}{6},\frac{5\pi}{3}$  

•  $x=\frac{\pi}{3},\frac{5\pi}{3}$  

•  $x=\frac{\pi}{3},\frac{7\pi}{6}$  

•  $No\ Solution$  

Solve the trigonometric equation below, exact answers only, for

 $0\le x<2\pi$  (This means RADIANS):

 $\sin x=\frac{\sqrt{2}}{2}$  

•  $x=\frac{\pi}{4},\frac{3\pi}{4}$  

•  $x=\frac{11\pi}{6}$  

•  $x=\frac{3\pi}{4}$  

•  $x=\frac{\pi}{4},\frac{7\pi}{6},\frac{11\pi}{6}$  

Solve the trigonometric equation below, exact answers only, for

 $0\le x<2\pi$  (This means RADIANS):

 $\cos x=-\frac{1}{2}$  

•  $x=\frac{4\pi}{3}$  

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

•  $x=\frac{3\pi}{4}$  

•  $x=\frac{2\pi}{3},\frac{4\pi}{3}$  

Solve the trigonometric equation below, exact answers only, for

 $0\le x<2\pi$  (This means RADIANS):

 $\sec x=-\frac{2}{\sqrt{3}}$  

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

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

•  $x=\frac{5\pi}{6}$  

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

Solve the trigonometric equation below, exact answers only, for

 $0\le x<2\pi$  (This means RADIANS):

 $\csc x=-1$  

•  $x=\frac{3\pi}{4}$  

•  $No\ Solution$  

•  $x=\frac{3\pi}{4},\frac{3\pi}{2}$  

•  $x=\frac{3\pi}{2}$  

Solve the trigonometric equation below, exact answers only, for

 $0\le x<2\pi$  (This means RADIANS):

 $-\frac{\sqrt{3}}{2}=\sin x$  

•  $x=\frac{4\pi}{3}$  

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

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

•  $x=\frac{7\pi}{6},\frac{11\pi}{6}$