Solving with Trigonometric Identities

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

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

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

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

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

• A
• B
• C
• D

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 the solution over the interval [0, 2π)

• 0, π, π/6, 5π/6,
• 0, π/6, 7π/6
• π, 5π/6, 11π/6
• π, π/6, 5π/6, 7π/6, 11π/6

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

CCSS.HSF.TF.B.7

Hint: Are the terms in the best order??

• A
• B
• C
• D

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

CCSS.HSF.TF.B.7

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

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

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

• θ = 0
• θ = π /2
• θ = π
• θ = 2π

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

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

Find the general solution of the equation.

• π/6; 11π/6

• π/6

• 11π/6

• π/3; 11π/3

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

CCSS.HSF.TF.B.7