Trigonometry Questions and Solutions for Matric

Master Matric Trigonometry with CAPS-aligned practice questions, identities and step-by-step solutions for South African Grade 12 students.

Trigonometry is the largest section of NSC Paper 2. This page focuses on identities, equations, the cosine and sine rules, and 2D/3D problems — the questions that appear most often in Matric exams. In Grade 12 the emphasis is on compound and double angles, general solutions and problems in two and three dimensions. Each solution below shows the reasoning a memo expects, including the quadrant or identity used at each step.

Practice questions with solutions

Solve for θ ∈ [0°, 360°]: sin θ = 0.5

  1. Reference angle = 30°
  2. sin positive in Q1 and Q2

Answer: θ = 30° or 150°

Prove: (1 − cos²x) / sin x = sin x

  1. 1 − cos²x = sin²x
  2. sin²x / sin x = sin x

Answer: Proven

In △ABC, a = 7, b = 9, C = 60°. Find c.

  1. Use cosine rule: c² = a² + b² − 2ab cos C
  2. c² = 49 + 81 − 126(0.5) = 67

Answer: c ≈ 8.19

Simplify: sin(180° + x) · tan(360° − x) / cos(90° + x)

  1. sin(180° + x) = −sin x and tan(360° − x) = −tan x
  2. cos(90° + x) = −sin x
  3. (−sin x)(−tan x) / (−sin x) = −tan x

Answer: −tan x

Find the general solution of cos x = −0.5

  1. The reference angle is 60°
  2. Cosine is negative in quadrants 2 and 3: x = 120° or x = 240°
  3. Add k·360°

Answer: x = ±120° + k·360°, k ∈ ℤ

Without a calculator, evaluate sin 15° cos 15°.

  1. sin 2A = 2 sin A cos A, so sin A cos A = ½ sin 2A
  2. sin 15° cos 15° = ½ sin 30° = ½ × ½

Answer: ¼

Find the area of △PQR if p = 8, q = 6 and R = 30°.

  1. Area = ½ pq sin R
  2. = ½ (8)(6)(0.5)

Answer: 12 square units

Solve for x ∈ [0°; 360°]: sin 2x = cos x

  1. 2 sin x cos x − cos x = 0
  2. cos x(2 sin x − 1) = 0
  3. cos x = 0 gives x = 90° or 270°
  4. sin x = ½ gives x = 30° or 150°

Answer: x = 30°, 90°, 150° or 270°

Tips

  • Know all reduction formulas.
  • Always state the quadrant when solving trig equations.
  • Factorise instead of dividing by a trig ratio, so that no solutions are lost.
  • Learn the special-angle values: many questions say 'without a calculator'.

Snap&Learn gives South African Matric learners instant, CAPS-aligned, step-by-step Mathematics solutions. Snap or upload a question and the AI shows every method mark the way the NSC memo awards them. Your first three AI solutions are free.