Trigonometric Equations

Math ⇒ Trigonometry

Trigonometric Equations starts at 11 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Trigonometric Equations. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 12

Find all solutions to the equation sin(2x) = 0 in the interval [0, 2π).

If cos(2x) = 1/2, what are the solutions for x in [0, 2π)?

If cos(x) = cos(β), what is the general solution for x?

If sin(x) = sin(α), what is the general solution for x?

If tan(x) = tan(γ), what is the general solution for x?

Solve the equation 2cos²(x) - 1 = 0 for x in [0, 2π).

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

Solve the equation 2sin²(x) - 1 = 0 for x in [0, 2π).

Which of the following is a general solution to the equation cos(x) = 0? (1) x = π/2 + nπ, n ∈ ℤ (2) x = nπ, n ∈ ℤ (3) x = π/4 + nπ, n ∈ ℤ (4) x = 2nπ, n ∈ ℤ

Which of the following is a solution to the equation sin(x) = -1? (1) x = 0 (2) x = π/2 (3) x = 3π/2 (4) x = π

Which of the following is NOT a solution to sin(x) = 0? (1) x = 0 (2) x = π (3) x = π/2 (4) x = 2π

Which of the following is the general solution to sin(x) = -1? (1) x = 3π/2 + 2nπ, n ∈ ℤ (2) x = π/2 + 2nπ, n ∈ ℤ (3) x = π + 2nπ, n ∈ ℤ (4) x = 0 + 2nπ, n ∈ ℤ

Fill in the blank: The equation cos(x) = 0.5 has solutions x = ________ and x = ________ in [0, 2π).

Fill in the blank: The equation cos(x) = -1 has solution x = ________, where n ∈ ℤ.

Fill in the blank: The equation tan(x) = 0 has solutions x = ________, where n ∈ ℤ.

Fill in the blank: The equation tan(x) = undefined at x = ________, where n ∈ ℤ.

True or False: The equation cos(x) = 0 has solutions at x = π/2, 3π/2, 5π/2, ...

True or False: The equation cos(x) = 2 has a real solution.

True or False: The equation sin(x) = 0.5 has exactly two solutions in the interval [0, 2π).

True or False: The equation sin(x) = 2 has a real solution.