Trigonometry Challenges

Trigonometry Challenges

  1. Solve the equation: 2cos^2(x) - sin(x) = 0 for x in the interval [0, 2π). Answer: x = 0, π/4, π/2

  2. Find all solutions to the equation: 4sin^3(x) + 2cos(3x) = 1 in the interval [0, 2π). Answer: x = π/6, 5π/6

  3. Solve the equation: tan(x) - √3 = 0. Answer: x = (2n+1)π/3, where n ∈ ℤ

  4. Determine all solutions for the equation: sin(x) = cos(x). Answer: x = π/4 + nπ, where n ∈ ℤ

  5. Find the solutions to the equation: 2sin^2(x) - 1 = 0 on the interval [0, 2π). Answer: x = π/2, 3π/2

  6. Solve the equation: cos(x) = 0. Answer: x = (2n + 1)π/2, n ∈ ℤ

  7. Determine where sin(x) = 0 in the interval [0, 2π). Answer: x = 0, π

  8. Solve the equation: cos(2x) + 1/2 = 0. Answer: x = (2nπ + π/3), where n ∈ ℤ

  9. Find all solutions for sin(2x) = √3/2. Answer: x = (4n + 1)π/6, (4n + 5)π/6, where n ∈ ℤ

  10. Solve the equation: tan(x) = 0. Answer: x = nπ, n ∈ ℤ

  11. Determine where sec(x) = 1 in the domain of real numbers. Answer: x = π/2 - 2nπ, n ∈ ℤ

  12. Solve the equation: 2sin^2(x) + sin(x) - 1 = 0 in [0, 2π). Answer: x = 7π/6, 11π/6

  13. Find all solutions to the equation: 1 - cos(2x) = 0 in the interval [0, 2π). Answer: x = 3π/4, 7π/4

  14. Determine all solutions for sin(x) = -1. Answer: x = nπ + π/2, n ∈ ℤ

  15. Solve the equation: cos(x) + √2/2 = 0 in [0, 2π). Answer: x = 5π/4, 7π/4