Trigonometry Trigonometric Equations

Question 1

What are all solutions to sin(x) = 0 on the interval [0, 2π)?

Accepted Answer

x = 0, π

Answer

x = 0, π/2

Answer

x = π/2, 3π/2

Answer

x = π, 3π/2

Question 2

Solve cos(x) = 1/2 for x in [0, 2π).

Accepted Answer

x = π/3, 5π/3

Answer

x = π/6, 5π/6

Answer

x = π/3, 2π/3

Answer

x = π/4, 7π/4

Question 3

What is the general solution for sin(x) = 1?

Accepted Answer

x = π/2 + 2nπ

Answer

x = nπ

Answer

x = 2nπ

Answer

x = π/2 + nπ

Question 4

Solve tan(x) = 1 for x in [0, 2π).

Accepted Answer

x = π/4, 5π/4

Answer

x = π/4, 3π/4

Answer

x = π/6, 7π/6

Answer

x = π/3, 4π/3

Question 5

Which of the following trigonometric equations has no real solution?

Accepted Answer

sin(x) = 2

Answer

sin(x) = 0.5

Answer

cos(x) = -1

Answer

tan(x) = 100

Question 6

Solve 2sin(x) − 1 = 0 for x in [0, 2π).

Accepted Answer