Trigonometric Equations

Solve
sinθ = √3/2

• θ = π /6, 5π /6

• θ = 2π /3, 4π /3

• θ = π /3, 2π /3

• θ = π /4, 3π /4

Solve the trigonometric equation in the interval  $\left(0,\ 2\pi\right]$ .

 $11\sin x+5=\sin x$  

•  $\frac{\pi}{3},\frac{2\pi}{3}$  

•  $\frac{\pi}{6},\frac{5\pi}{6}$  

•  $\frac{7\pi}{6},\frac{11\pi}{6}$  

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

Solve on the domain [0,2π)
cos x + 1 = 0

• 0
• No solution
• π
• 3π/2

Solve on the Interval [0,2π) 
   sinθ = -1   

• θ = π /2, 3π /2 
• θ = π /2
• θ = 3π /2
• θ = π  

• DNE

• π/4, 11π/6

• π/4, 7π/4

• π/6, π/4

• 7π/4, 11π/4

• π/6, 11π/6

• π/6, 7π/6, 11π/6

• 11π/6

• π/6, 5π/6

• 5π/4

• π/3, 5π/3

• No solution.

• 5π/3

• No solution.

• 5π/4

• π/3, 5π/3

• No solution.

• 5π/3