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Math 30-1 · Worksheets

Trigonometry · Set B

Ten questions of mixed difficulty, covering Trigonometry. Print it, or work through it on screen — the answer key starts on its own page.

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Trigonometry · Set B

Math 30-1 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. Using a sum identity, what is the exact value of sin 75°?

    1. a) (√6 + √2)/4
    2. b) (√6 − √2)/4
    3. c) √2/2 + 1/2
    4. d) (√3 + 1)/2

  2. What is 180° in radians?

    1. a) π
    2. b) π/2
    3. c) 180π
    4. d) 2π

  3. Solve sin θ = 1/2 for 0 ≤ θ < 2π.

    1. a) π/3 and 2π/3
    2. b) π/6 and 7π/6
    3. c) π/6 only
    4. d) π/6 and 5π/6

  4. What is the exact value of cos(4π/3)?

    1. a) −√3/2
    2. b) −1/2
    3. c) 1/2
    4. d) √3/2

  5. What is the period of y = 2 cos(3x), in radians?

    1. a) 3π
    2. b) 2π
    3. c) 2π/3
    4. d) 6π

  6. How many solutions does sin 2θ = 1/2 have for 0 ≤ θ < 2π?

    1. a) 6
    2. b) 4
    3. c) 2
    4. d) 8

  7. What is the exact value of sin 30°?

    1. a) √3/2
    2. b) √2/2
    3. c) 1
    4. d) 1/2

  8. What is the period of y = sin x, in radians?

    1. a) 2π
    2. b) π/2
    3. c) 4π
    4. d) π

  9. An angle in standard position has sin θ > 0 and cos θ < 0. Which quadrant is its terminal arm in?

    1. a) Quadrant II
    2. b) Quadrant III
    3. c) Quadrant I
    4. d) Quadrant IV

  10. What is the maximum value of y = 2 sin x + 5?

    1. a) 2
    2. b) 10
    3. c) 7
    4. d) 5

Answer key · Trigonometry · Set B

Math 30-1 · maddyhelps.com

  1. a) (√6 + √2)/4 — sin(45° + 30°) = sin 45° cos 30° + cos 45° sin 30° = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4. The minus version is sin 15°.
  2. a) π — Half a turn is π radians, so 180° = π. That one fact gives every conversion: multiply degrees by π/180.
  3. d) π/6 and 5π/6 — The reference angle is π/6, and sine is positive in Quadrants I and II: π/6 and π − π/6 = 5π/6. Stopping at one answer is the usual slip.
  4. b) −1/2 — 4π/3 is in Quadrant III with reference angle π/3. cos(π/3) = 1/2, and cosine is negative in Quadrant III, so −1/2.
  5. c) 2π/3 — The period is 2π ÷ |b| = 2π/3. The 2 in front changes the amplitude, never the period.
  6. b) 4 — The period of sin 2θ is π, so the graph completes two full cycles on [0, 2π). Each cycle hits 1/2 twice: 2 × 2 = 4.
  7. d) 1/2 — In the 30-60-90 triangle the side opposite 30° is half the hypotenuse, so sin 30° = 1/2. √3/2 is sin 60°.
  8. a) 2π — One full turn around the unit circle brings sine back to where it started, and a full turn is 2π.
  9. a) Quadrant II — Sine follows y and cosine follows x. Positive y with negative x is Quadrant II — the S in CAST, where only sine is positive.
  10. c) 7 — The midline is y = 5 and the amplitude is 2, so the graph peaks at 5 + 2 = 7 and bottoms out at 3.