maddyhelps

Math 30-1 · Worksheets

Trigonometry · Set A

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

All worksheets

Trigonometry · Set A

Math 30-1 · maddyhelps.com

Name
Date
Score
/ 10

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

  1. The point P(−3, 4) lies on the terminal arm of angle θ. What is cos θ?

    1. a) 3/5
    2. b) −4/3
    3. c) 4/5
    4. d) −3/5

  2. What is 180° in radians?

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

  3. A circle has radius 6 cm. What arc length does a central angle of 2π/3 cut off?

    1. a) 2π cm
    2. b) 4π cm
    3. c) 720 cm
    4. d) 12π cm

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

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

  5. Solve 2cos²θ − cos θ − 1 = 0 for 0 ≤ θ < 2π.

    1. a) 2π/3, 4π/3
    2. b) 0, π/3, 5π/3
    3. c) π, π/3, 5π/3
    4. d) 0, 2π/3, 4π/3

  6. Simplify (1 − cos²x) ÷ (sin x cos x).

    1. a) sin x
    2. b) cot x
    3. c) tan x
    4. d) 1

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

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

  8. What is the amplitude of y = 3 sin x?

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

  9. Which angle is coterminal with 45°?

    1. a) 135°
    2. b) −45°
    3. c) 225°
    4. d) 405°

  10. What is 3π/4 in degrees?

    1. a) 135°
    2. b) 270°
    3. c) 120°
    4. d) 150°

Answer key · Trigonometry · Set A

Math 30-1 · maddyhelps.com

  1. d) −3/5 — First find r = √((−3)² + 4²) = 5. Then cos θ = x/r = −3/5. The sign comes from x, which is negative in Quadrant II.
  2. a) π — Half a turn is π radians, so 180° = π. That one fact gives every conversion: multiply degrees by π/180.
  3. b) 4π cm — Arc length is a = rθ with θ in radians: 6 × 2π/3 = 4π cm. Using 120° instead of radians gives the nonsense 720.
  4. 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.
  5. d) 0, 2π/3, 4π/3 — Treat it as a quadratic in cos θ: (2cos θ + 1)(cos θ − 1) = 0. cos θ = −1/2 gives 2π/3 and 4π/3; cos θ = 1 gives 0. Dropping the 0 is the common miss.
  6. c) tan x — The Pythagorean identity turns 1 − cos²x into sin²x. Then sin²x ÷ (sin x cos x) = sin x ÷ cos x = tan x.
  7. c) −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.
  8. c) 3 — The amplitude is |a|, the distance from the midline to a peak: 3. The full height from trough to peak would be 6.
  9. d) 405° — Coterminal angles differ by full turns: 45° + 360° = 405°. −45° is a reflection across the x-axis, not the same arm.
  10. a) 135° — Replace π with 180°: 3 × 180° ÷ 4 = 135°.