Solving Trigonometric Equations Algebraically

Solve
2cos²θ -1=0
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

• A
• B
• C
• D

Solve

sin²θ = 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

Find all solutions.

2cos(3πx) + 5 = 4

• x = 5/18 + 2n/3 and x = 11/18 + 2n/3

• x = 1/9 + 2n/3 and x = 5/9 + 2n/3

• x = 2/9 + 2πn and x = 4/9 + 2πn

• x = 2/9 + 2n/3 and x = 4/9 + 2n/3

For what numbers x, 0 e x e2 ext{π} , does sin x= -1

• π/2, 3π/2

• 3π/2

• none

For what numbers x, 0≤x≤2π, does sin x =1

• π/2, 3π/2

• π/2

• 0, 2

• none

For what numbers x, 0 e x e2 ext{π} does sin x= -1

• π/2, 3π/2

• 3π/2

• none

For what numbers x, 0 e x e2 ext{π} , does sin x= -1

• π/2, 3π/2

• 3π/2

• none

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

• θ = 0

• θ = π /2

• θ = π

• θ = 2π

For what numbers x, 0 e x e2 \pi, does sin x =1

• π/2, 3π/2

• π/2

• 0, 2

• none