Grade 11 Maths · Functions · Paper 1

Trigonometric Functions Grade 11

Real Trigonometric Functions past paper questions and answers from 2024 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: 42 past paper questions
skills: 6 skills
videos: 6 videos

Try a Trigonometric Functions exam question

No sign-up. Takes 3 minutes.

Question 4.2 · March 2025 · Provincial · 3 marks

4.2 If

tan α = \frac{3}{4}

where

9 0^{\circ} < α < 27 0^{\circ}

. Determine, with the aid of a diagram, the value of

cos α

.(3)

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

Trigonometric Functions skills

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

More Trigonometric Functions Grade 11 questions and answers

Try each one on paper before you open the memo.

4. Question 3.1.3 · March 2025 · Paper 1 · Provincial · 3 marks
In the diagram, $P (- 6; 8)$ is a point in the Cartesian plane. $A$ is the point on the positive x-axis. $∠ A OP = θ$ .
3.1 Determine, with the aid of a diagram, the following:
3.1.3 $sin θ + cos θ$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Substitution for $sin θ$ $sin θ = \frac{8}{10}$
  1 mark · Find trig ratios from a sketch
2. ✓
  Substitution for $cos θ$ $cos θ = - \frac{6}{10}$
  1 mark · Find trig ratios from a sketch
3. ✓
  Answer $\frac{8}{10} - \frac{6}{10} = \frac{1}{5}$
  1 mark · Find trig ratios from a sketch
5. Question 2.3.1 · June 2024 · Paper 2 · Provincial · 4 marks
2.3 Given: $k sin β = - 5$ and $k cos β - 1 = 0$ where $k > 0$ .
2.3.1 Explain why $β \in [27 0^{\circ}; 36 0^{\circ}]$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Isolate sin beta $sin β = - \frac{5}{k}$
  1 mark · Solve a linear equation
2. ✓
  Isolate cos beta $cos β = \frac{1}{k}$
  1 mark · Solve a linear equation
3. ✓
  DiagramSketch: terminal arm through the point $(1; - 5)$ with $r = k$ , in quadrant IV (see diagram).
  1 mark · Decide the quadrant and sign
4. ✓
  ExplanationSince $k > 0$ : $sin β$ is negative and $cos β$ is positive, which happens only in quadrant IV, so $β \in [27 0^{\circ}; 36 0^{\circ}]$ . OR In quadrant IV, $y$ is negative and $x$ is positive.
  1 mark · Decide the quadrant and sign
6. Question 3.1 · June 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, the graphs of $f (x) = a cos x$ and $g (x) = sin (x + p)$ are drawn for $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
3.1 Determine the values of $a$ and $p$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify a from amplitudeAt $x = 0^{\circ}$ , $f (0) = - 2$ (amplitude 2, reflected), so $a = - 2$
  1 mark · Find equation of a trig graph
2. ✓
  Identify p from shift $g$ is $y = sin x$ shifted $3 0^{\circ}$ right (it cuts the $x$ -axis at $3 0^{\circ}$ and $- 15 0^{\circ}$ ): $g (x) = sin (x - 3 0^{\circ})$ , so $p = - 3 0^{\circ}$
  1 mark · Find equation of a trig graph
7. Question 3.1.2 · March 2024 · Paper 1 · Provincial · 3 marks
Do not use a calculator when answering Question 3.
In the diagram, $P (- 6; 8)$ is a point in the Cartesian plane. A is a point on the positive x-axis. $∠ A OP = θ$ .
3.1 Determine, with the aid of the diagram, the following:
3.1.2 $sin θ + cos θ$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Determine ratios $sin θ = \frac{y}{r} = \frac{8}{10}$
  $cos θ = \frac{x}{r} = \frac{- 6}{10}$
  2 marks · Find trig ratios from a sketch
2. ✓
  Calculate sum $\frac{8}{10} - \frac{6}{10} = \frac{2}{10} = \frac{1}{5}$
  1 mark · Find trig ratios from a sketch
8. Question 3.1.2 · June 2024 · Paper 2 · Provincial · 2 marks
3.1 If $θ = 89, 4^{\circ}$ and $α = 12 2^{\circ}$ , evaluate the following (round off answers correct to three decimal places):
3.1.2 $\frac{t a n α}{c o s ^{2} ( θ + α )}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution $\frac{t a n 12 2 ^{\circ}}{c o s ^{2} ( 89 , 4 ^{\circ} + 12 2 ^{\circ} )} = \frac{t a n 12 2 ^{\circ}}{( c o s 211 , 4 ^{\circ} ) ^{2}}$
  1 mark · Calculate trig values on a calculator
2. ✓
  Answer $= - 2, 197$
  1 mark · Calculate trig values on a calculator
9. Question 4.1 · June 2024 · Paper 2 · Provincial · 6 marks
Given: $f (x) = sin 2 x$ and $g (x) = 3 cos x$ for $x \in [- 9 0^{\circ}; 9 0^{\circ}]$
4.1 Sketch the graphs of $f (x)$ and $g (x)$ on the same system of axes in the given interval.

Show all coordinates of the intercepts and the turning points.(6)
Show the memo (6 ticks)Memo
1. ✓
  Shape of fSine curve completing one full wave on $[- 9 0^{\circ}; 9 0^{\circ}]$
  1 mark · Sketch a trig graph
2. ✓
  Turning points of f $(- 4 5^{\circ}; - 1)$ and $(4 5^{\circ}; 1)$
  1 mark · Sketch a trig graph
3. ✓
  f passes through the origin $(0; 0)$
  1 mark · Sketch a trig graph
4. ✓
  Shape of gCosine curve with amplitude 3, above the x-axis on $[- 9 0^{\circ}; 9 0^{\circ}]$
  1 mark · Sketch a trig graph
5. ✓
  Turning point of g $(0; 3)$
  1 mark · Sketch a trig graph
6. ✓
  End points of f and gBoth graphs end at $(- 9 0^{\circ}; 0)$ and $(9 0^{\circ}; 0)$
  1 mark · Sketch a trig graph
10. Question 6.2 · November 2024 · Paper 2 · Provincial · 2 marks
The graph of $f (x) = cos (x + 30°)$ in the interval of $x \in [- 120°; 150°]$ has been drawn in the diagram below. $Diagram for this question$
6.2 Write down the range of $h (x) = f (x + 60°) + 1$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Correct interval $0$ to $2$
  1 mark · Find trig graph amplitude and range
2. ✓
  Correct notation $y \in [0; 2]$ or $0 \leq y \leq 2$
  1 mark · Find trig graph amplitude and range

Trigonometric Functions Grade 11 videos

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

Functions : Horizontal Translations - Horizontal Shift - y = f(x - c) Examples and ExplanationRadford Mathematics

Reflections of the Exponential GraphMaths101 with Jana van Niekerk

Trigonometry Graphs grade 10: How to drawKevinmathscience

Trig functions grade 11 and 12: DrawKevinmathscience

Trig functions grade 11 and 12: Determine EquationKevinmathscience

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills