6.3 Solving Trigonometric Equations

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

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

Solve for 0≤x≤2π

2cos²x + cosx = 0

• π/2, 3π/2

• 0, π,2π

• 2π/3, 4π/3

• π/3, 5π/3

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

CCSS.HSF.TF.B.7

Solve for 0≤x≤2π

4cos²x - 2 = 0

• π/3, 5π/3

• π/4, 7π/4

• 3π/4, 5π/4

• π/6, 11π/6

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.TF.A.3

Solve for 0≤x≤2π

sinxtanx = sinx

• π/2, 3π/2

• 3π/4, 7π/4

• 0, π, 2π

• π/4, 5π/4

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

CCSS.HSF.TF.B.7

Solve for 0≤x≤2π

2sin²x - 5sinx + 2 = 0

• π/6, 5π/6

• 7π/6, 11π/6

• π/3, 2π/3

• 4π/3, 5π/3

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

CCSS.HSF.TF.B.7

Solve for 0≤x≤2π

3sin²x + sinx - 4 = 0

• 0, π

• π/2

• π/6, 5π/6

• 3π/2

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.TF.B.7

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

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

Find all solutions.

2sin(6x) + √3 = 0

• x = π/18 + πn/3 and x = 5π/18 + πn/3

• x = 11π/18 + 2πn and x = 7π/18 + 2πn

• x = 4π/18 + πn/3 and x = 5π/18 + πn/3

• x = 4π/3 + 2πn and x = 5π/3 + 2πn

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.4

CCSS.HSF.TF.B.7

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

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

Which of the following is the solution of sin²x + cos²x = 2?

• 0

• π/4

• π/6

• no solution

Tags

CCSS.HSA.REI.A.1

CCSS.HSF.TF.C.8