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Trigonometric Functions · Ages 16–17

Basic Trigonometric Equations Practice

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Designed for 11th grade math students. Solve each equation for all real numbers or within the specified interval, showing your reference angle and quadrant work.

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

  2. Solve cos x = -sqrt(2)/2 for x in [0, 2π).

  3. Find the general solution in radians: tan x = sqrt(3).

  4. Solve cos x = 1.4 for real solutions.

  5. Find the general solution in radians: 2 sin x + sqrt(3) = 0.

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

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Basic Trigonometric Equations Practice

Answer key

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

    x = π/6, 5π/6

  2. Solve cos x = -sqrt(2)/2 for x in [0, 2π).

    x = 3π/4, 5π/4

  3. Find the general solution in radians: tan x = sqrt(3).

    x = π/3 + πk, where k is an integer

  4. Solve cos x = 1.4 for real solutions.

    No real solutions, because the cosine ratio must be between -1 and 1.

  5. Find the general solution in radians: 2 sin x + sqrt(3) = 0.

    x = 4π/3 + 2πk and x = 5π/3 + 2πk, where k is an integer

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

    x = π/4, 5π/4