cvu2023 14M General solution of trigonometric equations

14M General solution of trigonometric equations

Multiple Choice

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

• π/12, 5π/12

• π/6, 5π/6

• π/6

• π/3

Multiple Choice

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

• x = π/3, 5π/3

• x = π/2, 3π/2

• x = π/6, 5π/6

• x = π/4, 7π/4

Multiple Choice

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

• -π/3, 2π/3

• 4π/3

• π/3, 5π/6

• 3π/4, 7π/4

Multiple Choice

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

Multiple Choice

Find the general solution for sin(x) = 0.5

• π/6, 5π/6

• 2nπ+ π/6, (2n+1) - π/6

  where n ∈ Z

• 2nπ - π/6, (2n+1) + π/6

  where n ∈ Z

• 2nπ ± π/6

  where n ∈ Z

Multiple Choice

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

• x = 2nπ - π/3 ,

  (2n+1) + π/3

  n ∈ Z

• x = 2nπ + π/6 ,

  (2n+1) - π/6

  n ∈ Z

• x = 2nπ ± π/6

  n ∈ Z

• x = (2n+1)π ± π/3

  n ∈ Z

Multiple Choice

Find the general solution for tan(x) = 1

• x = 2nπ ± π/4

  n ∈ Z

• x = πn + π/4

  n ∈ Z

• x = πn + π/3

  n ∈ Z

• x = π/4, 5π/4

Multiple Choice

Find all the general solution for tan(x) = - 1

• x = 2nπ ± π/4

  n ∈ Z

• x = (2n+1) π - π/4

  n ∈ Z

• x = πn + π/3

  n ∈ Z

• x = nπ - π/4

  n ∈ Z

Multiple Choice

Find all the general solution for tan(x/2) = - 1

• x = 2nπ - π/2

  n ∈ Z

• x = (2n+1) π - π/4

  n ∈ Z

• x = πn + π/3

  n ∈ Z

• x = nπ - π/4

  n ∈ Z

Multiple Choice

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

• x = nπ/4

• x = nπ

• x = nπ/2

• x = nπ/3