Solving Trig Equations

Solve
cos²θ = ½ 
on θ∈[0, 2π)

• θ = π /4, 7π /4
• θ = π /4, 3π /4
• θ = 3π /4, 5π /4
• θ = π /4, 3π /4, 5π /4, 7π /4

Solve on the Interval [0,2π)
tan(x)+1=2

• 0 and π  
• 3π/4 and 7π/4
• π/4 and 5π/4
• 3π/4 and 5π/4

2 sinθ+3=2

• π/6,2π/3
• 7π/6 
• 7π/6, 11π/6

Solve on the domain [0, 2π)
1/2sec x - 1 = 0

• π/6, 5π/6
• π/3, 5π/3
• 2π/3, 4π/3
• 7π/6, 11π/6

Solve on the domain [0, 2π)
4sin²x = 3

• π/6, 11π/6
• π/3, 2π/3
• π/6, 5π/6, 7π/6, 11π/6
• π/3, 2π/3, 4π/3, 5π/3

Solve on the domain [0, 2π)
2sin x cos x = √2 cos x

• π/2, 3π/2
• 0, π/4, 3π/4
• π/2, 3π/2, π/4, 3π/4
• No solution

Solve on the domain [0, 2π)
cos² x + sin x + 1 = 0

• π
• 3π/2
• π/6, 5π/6, 3π/2
• No solution

Solve on the domain [0, 2π)
cos x + 2 = 3 cos x

• 0, 2π/3, 4π/3
• π
• 0
• No solution

Solve on the domain [0,2π)
1/4sin x + 1= 0

• 0
• 7π/4
• 5π/4
• No solution

Solve  $3\sin^2x=7\sin^2x+4\sin x+1$  over  $\left[0,2\pi\right)\$  

•  $x=\left\{\frac{7\pi}{6}\right\}$  

•  $x=\left\{0,\ \frac{\pi}{3},\ \frac{5\pi}{3}\right\}$  

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

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