Trigonometry Trigonometric Equations

Question 1

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

Accepted Answer

x = 0, π

Answer

sin(x) = 0 at multiples of π, so on [0, 2π) the solutions are x = 0 and x = π.

Question 2

Solve cos(x) = 1/2 for x in [0, 2π).

Accepted Answer

x = π/3, 5π/3

Answer

cos(x) = 1/2 at x = π/3 (Q1) and x = 5π/3 (Q4) since cosine is positive in quadrants I and IV.

Question 3

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

Accepted Answer

x = π/2 + 2nπ

Answer

sin(x) = 1 only at x = π/2, and since sine has period 2π, the general solution is x = π/2 + 2nπ.

Question 4

Solve tan(x) = 1 for x in [0, 2π).

Accepted Answer

x = π/4, 5π/4

Answer

tan(x) = 1 at x = π/4 (Q1) and x = 5π/4 (Q3) since tangent is positive in quadrants I and III.

Question 5

Which of the following trigonometric equations has no real solution?

Accepted Answer

sin(x) = 2

Answer

The range of sin(x) is [-1, 1], so sin(x) = 2 has no real solution.

Trigonometry Practice Test