Grade 12 Maths · Paper 2

Trigonometry Grade 12

Real 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: 85 past paper questions
skills: 14 skills
videos: 14 videos

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Question 5.2 · March 2025 · Provincial · 6 marks

5.2 Simplify:

\frac{s i n ( - 18 0 ^{\circ} - θ ) \cdot t a n ( 18 0 ^{\circ} - θ ) \cdot c o s ( - θ )}{c o s ^{2} ( 9 0 ^{\circ} + θ ) + 3 s i n ^{2} θ}

(6)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

What's in Trigonometry Grade 12

Each skill is one thing a memo gives a tick for. Tap a skill for its own questions, notes and videos.

Compound Angles21 past paper questions

Double Angles6 past paper questions

Use a double angle identityRewrite trig ratios of double angles, for example sin 2A = 2 sin A cos A and cos 2A = 1 − 2 sin²A, choosing the form that helps.24 past paper questions · 3 videos

Trigonometric Identities using Double Angles21 past paper questions

Trigonometric Equations20 past paper questions

Two and Three Dimensional Trigonometry19 past paper questions

More Trigonometry Grade 12 questions and answers

Try each one on paper before you open the memo.

1. Question 6.2.3 · May/June 2025 · Paper 2 · National (DBE) · 5 marks
6.2 Consider the expression: $sin (A - B) - sin (A + B)$
6.2.3 Hence, determine the solution for $sin 4 x - sin 10 x = sin 3 x$ for $x \in [0^{\circ}; 3 0^{\circ}]$ .(5)
Show the memo (3 ticks)Memo
1. ✓
  Substitute the simplified term and factorize $- 2 cos 7 x sin 3 x = sin 3 x$
  $2 cos 7 x sin 3 x + sin 3 x = 0$
  $sin 3 x (2 cos 7 x + 1) = 0$
  2 marks · Take out a common factor
2. ✓
  Set each factor to zero $sin 3 x = 0$ OR $2 cos 7 x + 1 = 0$
  $sin 3 x = 0$ OR $cos 7 x = - \frac{1}{2}$
  1 mark · Solve a quadratic by factorising
3. ✓
  Solve for x in the given intervalFor $sin 3 x = 0$ :
  $3 x = 0^{\circ} + k \cdot 18 0^{\circ}$
  $x = 0^{\circ}$
  
  For $cos 7 x = - \frac{1}{2}$ (reference angle is $6 0^{\circ}$ , cosine is negative in 2nd quadrant):
  $7 x = 18 0^{\circ} - 6 0^{\circ} = 12 0^{\circ}$
  $x = \frac{12 0 ^{\circ}}{7} \approx 17, 1 4^{\circ}$
  
  Other general solutions will fall outside the $[0^{\circ}; 3 0^{\circ}]$ domain restriction.
  
  $x = 0^{\circ}$ or $x = 17, 1 4^{\circ}$
  2 marks · Find solutions in an interval
2. Question 5.3.1 · March 2025 · Provincial · 2 marks
5.3 A piece of land has the form of a quadrilateral ABCD with $A B = 20 m$ , $BC = 12 m$ and $C D = 7 m$ . $\hat{B} = 11 0^{\circ}$ and $\hat{C D A} = 7 1^{\circ}$ . The owner decides to divide the land into two plots by erecting a fence from A to C.
5.3.1 Calculate the length of the fence AC correct to one decimal place.(2)
Show the memo (2 ticks)Memo
1. ✓
  Apply Cosine Rule $A C^{2} = 1 2^{2} + 2 0^{2} - 2 (12) (20) cos 11 0^{\circ}$
  1 mark · Use the cosine rule
2. ✓
  Calculate length $A C^{2} = 708, 17...$
  $A C = 26, 61 m$
  1 mark · Use the cosine rule
3. Question 6.1.2 · March 2024 · Paper 1 · Provincial · 3 marks
6.1 Given: $tan x = \frac{3}{4}$ where $x \in [18 0^{\circ}; 27 0^{\circ}]$ . With the aid of a sketch, and without the use of a calculator, calculate:
6.1.2 $2 - sin 2 x$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Expand double angle $2 - 2 sin x cos x$
  1 mark · Use a double angle identity
2. ✓
  Substitute values $2 - 2 (\frac{- 3}{5}) (\frac{- 4}{5})$
  $= 2 - \frac{24}{25}$
  1 mark · Find trig ratios from a sketch
3. ✓
  Calculate final answer $\frac{26}{25} = 1, 04$
  1 mark · Find trig ratios from a sketch
4. Question 7.1.1 · March 2024 · Paper 1 · Provincial · 3 marks
7.1 Given: $cos (A - B) = cos A cos B + sin A sin B$
7.1.1 Use the above identity to deduce that $sin (A + B) = sin A cos B + cos A sin B$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Use co-ratios to convert sine to cosine $sin (A + B) = cos [9 0^{\circ} - (A + B)]$
  $= cos [(9 0^{\circ} - A) - B]$
  1 mark · Use co-ratio identities
2. ✓
  Apply given cosine difference identity $cos (9 0^{\circ} - A) cos B + sin (9 0^{\circ} - A) sin B$
  1 mark · Use a compound angle identity
3. ✓
  Convert back using co-ratios $sin A cos B + cos A sin B$
  1 mark · Use co-ratio identities
5. Question 7.1.1 · March 2023 · Provincial · 2 marks
Given $cos 4 0^{\circ} = t$ .
7.1 Without using a calculator, determine each of the following in terms of t.
7.1.1 $tan 4 0^{\circ}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Draw diagram or use identityDiagram with angle 40, adj t, hyp 1. Opp $1 - t^{2}$ .
  1 mark · Use the theorem of Pythagoras
2. ✓
  Write ratio $tan 4 0^{\circ} = \frac{1 - t ^{2}}{t}$
  1 mark · Find trig ratios from a sketch

Trigonometry Grade 12 videos

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

Grade 11 Trigonometry Reduction with Co-FunctionsMiss Martins Maths and Science

Compound Angles Grade 12Kevinmathscience

Grade 11 Trigonometry Identities IntroductionMiss Martins Maths and Science

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