Solving Trig Equations and Identities

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

• π / 3
• 2π / 3
• 5π / 3
• 7π / 3

Solve sinθ = ½ on θ∈[0, 2π)

• θ = π / 6,  7π / 6
• θ = π / 6,  5π / 6
• θ = 5π / 6,  7π / 6
• θ = 7π / 6,  11π / 6

Solve
cos θ = -1
on  θ∈[0, 2π)

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

Which of these is NOT
 a solution to
tan θ = 0 ?

• θ = 0
• θ = π /2
• θ = π
• θ = 2π

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
cosθ = - √(3)/2  
on θ∈[0, 2π)

• θ = π /3, 2π /3
• θ = 2π /3, 4π /3
• θ = π /6, 5π /6
• θ = 5π /6, 7π /6

• No solution
• π/3 +2πn, 5π/3 +2πn
• π/6 +2πn, 11π/6 +2πn
• 2π/3 +2πn, 4π/3 +2πn

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

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

• -cos²x = 0

• cosx(2cosx + 3) = 0

• cosx(2cosx − 3) = 0

• cos x = ⅔