Trigonometric Equations General Solutions cvu2023

Solve the equation 2sin(2x) - 1 = 0 for x in the interval [0, π].

• π/6, 5π/6

• π/12, 5π/12

• π/3, 5π/3

• π/3

Solve the equation 2cos(2x) = 1 for x in the interval [0, 2π].

• x = π/3, 5π/3

• x = π/6, 5π/6

• x = π/6, 11π/6

• x = π/4, 7π/4

Solve the equation 2cos(2x) = 1 for x in the interval [0, 2π].

• x = π/3, 5π/3

• x = π/6, 5π/6

• x = π/6, 11π/6

• x = π/4, 7π/4

Find the general solution for sin(x) = 0.5

• π/6, 5π/6

• 2n+ π/6, (2n+1) - π/6

  where n ∈ Z

• 2n - π/6, (2n+1) + π/6

  where n ∈ Z

• 2nπ ± π/6

  where n ∈ Z

Solve the equation tan(2x) = -√3 for x in the interval [0, 2π].

• -π/3, 2π/3

• π/3, 4π/3

• 2π/6, 5π/6

• 3π/4, 7π/4

Determine the general solution of the equation tan(x) = √3.

• x = π/3 + nπ

• x = π/6 + nπ

• x = π/2 + nπ

• x = π/4 + nπ

Solve the equation tan(x) = -1 for x in the interval [0, 2π].

• x = 3π/4, 7π/4

• x = π/2, 3π/2

• x = π/3, 4π/3

• x = π/4, 5π/4

Find the general solution of the equation cos(3x) = -1/2.

• x = (2π/3 + 2πn)/3

• x = (π/6 + 2πn)/3

• x = (4π/3 + 2πn)/3

• x = (π/3 + 2πn)/3

Find the general solution of the equation sin(x) = 0.

• x = nπ/4

• x = nπ

• x = nπ/2

• x = nπ/3