Grade 11 Maths · Trigonometry · Paper 2

Trigonometric Equations Grade 11

Real Trigonometric Equations past paper questions and answers from 2023 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 11 past paper questions
skills: 3 skills
videos: 3 videos

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Question 5.1 · March 2025 · Provincial · 5 marks

5.1 Determine the general solution

cos 2 θ = - \frac{1}{2}

(5)

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Trigonometric Equations skills

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More Trigonometric Equations Grade 11 questions and answers

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4. Question 4.5.2 · November 2025 · Paper 2 · Provincial · 2 marks
4.5 Given the identity: $tan β - sin β . cos β = tan β . sin^{2} β$
4.5.2 For which value(s) of $β$ will the identity in QUESTION 4.5 be undefined in the interval $β \in [- 180°; 180°]$ ?(2)
Show the memo (2 ticks)Memo
1. ✓
  $β = - 90°$ $β = - 90°$
  1 mark · Find solutions in an interval
2. ✓
  $β = 90°$ $β = 90°$
  1 mark · Find solutions in an interval
5. Question 2.4.2 · June 2024 · Paper 2 · Provincial · 4 marks
2.4 Given the identity: $sin^{2} α (tan α + \frac{1}{t a n α}) = tan α$
2.4.2 Hence or otherwise, determine the general solution of: $sin^{2} α (tan^{2} α + 1) = 3 tan α$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Divide both sides by tan alpha $sin^{2} α (tan^{2} α + 1) = 3 tan α$ . Divide by $tan α$ : $sin^{2} α (tan α + \frac{1}{t a n α}) = 3$
  1 mark · Simplify an algebraic fraction
2. ✓
  Substitute the identity: LHS = tan alphaBy 2.4.1 the left side is $tan α$ , so $tan α = 3$
  1 mark · Write tan as sin over cos
3. ✓
  General solution $α = 6 0^{\circ} + k \cdot 18 0^{\circ}$
  1 mark · Write the general solution
4. ✓
  k is an integer $k \in Z$
  1 mark · Write the general solution
6. Question 6.1 · November 2024 · Paper 2 · Provincial · 5 marks
6.1 Solve the following equation for $x \in [- 180°; 180°]$ .

$cos (x - 30°) = sin x$ (5)
Show the memo (5 ticks)Memo
1. ✓
  $sin x = cos (90° - x)$ $cos (x - 30°) = sin x$
  $cos (x - 30°) = cos (90° - x)$
  1 mark · Use co-ratio identities
2. ✓
  Equation with $k .360°$ $x - 30° = 90° - x + k .360°$ ; $k \in Z$
  1 mark · Write the general solution
3. ✓
  $x = 60° + k .180°$ $2 x = 120° + k .360°$
  $x = 60° + k .180°$
  1 mark · Write the general solution
4. ✓
  $k \in Z$ $k \in Z$
  1 mark · Write the general solution
5. ✓
  Solutions in the interval $x \in {- 120°; 60°}$
  1 mark · Find solutions in an interval
7. Question 4.2 · March 2023 · Paper 1 · Provincial · 3 marks
4.2 Solve for x, where $x \in [0^{\circ}; 36 0^{\circ}]$ : $sin x = - 0, 4$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Determine reference angleRef angle $= sin^{- 1} (0, 4) \approx 23, 5 8^{\circ}$
  1 mark · Calculate an angle from a ratio
2. ✓
  Find solutions in correct quadrants (3rd and 4th) $x = 18 0^{\circ} + 23, 5 8^{\circ} = 203, 5 8^{\circ}$
  $x = 36 0^{\circ} - 23, 5 8^{\circ} = 336, 4 2^{\circ}$
  2 marks · Find solutions in an interval

Trigonometric Equations Grade 11 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Trig Triangles Grade 10: Find angleKevinmathscience

General and Specific Solution grade 11:Part 1Kevinmathscience

General and Specific Solution grade 11: Part 2Kevinmathscience

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