Grade 10 Maths · Trigonometry · Sketch a trig graph

Trigonometric Graphs Grade 10

Draw a sine, cosine or tangent graph with the right shape, turning points, intercepts and asymptotes, for example y = 2 x for 0^ x 360^.

questions use it, all grades · 20 past paper, 51 practice: 71 questions use it, all grades · 20 past paper, 51 practice
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Trigonometry Graphs grade 10: How to drawKevinmathscience

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Question 7.2 · November 2025 · Paper 2 · National (DBE) · 3 marks

In the diagram, the graph of

f (x) = cos 2 x

is drawn for

x \in [- 135°; 135°]

. $Diagram for this question$

7.2 On the set of axes provided in the ANSWER BOOK, draw the graph of

g (x) = tan 2 x - 1

for

x \in [- 135°; 135°]

.(3)

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

More past paper questions: sketch a trig graph

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3. Question 7.3.2 · November 2024 · Paper 2 · National (DBE) · 3 marks
In the diagram below, the graph of $f (x) = tan x$ is drawn for the interval $x \in [- 180°; 180°]$ . $Diagram for this question$
7.3 Given: $g (x) = cos 2 x + 1$
7.3.2 On the grid given in the ANSWER BOOK, draw the graph of $g (x) = cos 2 x + 1$ for the interval $x \in [- 180°; 180°]$ . Clearly show the intercepts with the axes as well as the coordinates of the turning points.(3) $Diagram for question 7.3.2$
Show the memo (3 ticks)Memo
1. ✓
  Turning points on the x-axis: x = −90° ; 90°Minimum turning points (on the $x$ -axis) at $(- 90°; 0)$ and $(90°; 0)$
  1 mark · Sketch a trig graph
2. ✓
  ShapeCosine shape with period $180°$ , from $(- 180°; 2)$ to $(180°; 2)$ $Memo diagram$
  1 mark · Sketch a trig graph
3. ✓
  Turning point on the y-axis at (0 ; 2)Maximum turning point (and $y$ -intercept) at $(0; 2)$
  1 mark · Sketch a trig graph
4. Question 6.2.3 · November 2017 · Paper 2 · National (DBE) · 5 marks
6.2 Consider the functions $f (x) = sin (x - 30°)$ and $g (x) = cos 2 x$
6.2.3 On the grid provided in the ANSWER BOOK, draw the graphs of $f$ and $g$ for $x \in [- 90°; 180°]$ .
Clearly show ALL intercepts with the axes, turning points and end points.(5) $Diagram for question 6.2.3$
Show the memo (5 ticks)Memo
1. ✓
  $f$ : $x$ -intercept at $30°$ $f$ cuts the $x$ -axis at $x = 30°$ . $Memo diagram$
  1 mark · Sketch a trig graph
2. ✓
  Shape of $f$ $f$ : sine shape shifted $30°$ right, from $(- 90°; - 0, 87)$ through the minimum $(- 60°; - 1)$ , $(0°; - 0, 5)$ , the maximum $(120°; 1)$ , to the end point $(180°; 0, 5)$ .
  1 mark · Sketch a trig graph
3. ✓
  $g$ : $x$ -intercepts at $45°$ and $135°$ $g$ cuts the $x$ -axis at $x = - 45°$ , $45°$ and $135°$ .
  1 mark · Sketch a trig graph
4. ✓
  Shape of $g$ $g$ : cosine shape with period $180°$ , from $(- 90°; - 1)$ up to $(0°; 1)$ , down to $(90°; - 1)$ and up to $(180°; 1)$ .
  1 mark · Sketch a trig graph
5. ✓
  Turning point at $(90°; - 1)$ Turning point of $g$ at $(90°; - 1)$ .
  1 mark · Sketch a trig graph
5. Question 7.3 · September 2026 · Paper 2 · Provincial · 3 marks
Given: $f (x) = a cos (x + p)$ where $x \in [- 180°; 180°]$ $Diagram for this question$
7.3 Sketch the graph of $g (x) = - sin x$ , where $x \in [- 180°; 180°]$ , on the grid provided in the ANSWER BOOK. Clearly indicate intercepts with the axes.(3)
Show the memo (3 ticks)Memo
1. ✓
  Correct turning pointsTurning points $(- 90°; 1)$ and $(90°; - 1)$ $Memo diagram$
  1 mark · Sketch a trig graph
2. ✓
  Correct interceptsIntercepts at $(- 180°; 0)$ , $(0; 0)$ and $(180°; 0)$
  1 mark · Sketch a trig graph
3. ✓
  ShapeSmooth sine-shaped curve decreasing through the origin
  1 mark · Sketch a trig graph
6. Question 7.3 · September 2026 · Paper 2 · Provincial · 4 marks
In the diagram, the graph of $f (x) = sin 2 x$ is drawn for $x \in [- 180°; 180°]$ . $Diagram for this question$
7.3 On the set of axes provided in the ANSWER BOOK, draw the graph of $g (x) = - cos (x - 45°)$ for $x \in [- 180°; 180°]$ . Clearly show ALL the intercepts with the axes and the coordinates of the turning point.(4)
Show the memo (4 ticks)Memo
1. ✓
  ShapeA negative cosine curve shifted $45°$ to the right, drawn from $x = - 180°$ to $x = 180°$ : it starts at $(- 180°; \frac{2}{2})$ , rises to a maximum, falls to a minimum and rises to $(180°; \frac{2}{2})$ . $Memo diagram$
  1 mark · Sketch a trig graph
2. ✓
  Turning pointsMaximum $(- 135°; 1)$ and minimum $(45°; - 1)$
  1 mark · Sketch a trig graph
3. ✓
  x-intercepts $(- 45°; 0)$ and $(135°; 0)$
  1 mark · Sketch a trig graph
4. ✓
  y-intercept $(0; - \frac{2}{2})$
  1 mark · Sketch a trig graph

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