Grade 10 Maths · Functions

Sketch a trig graph

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

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Question 6.2 · November 2024 · Paper 2 · Provincial · 5 marks

6.2 Draw the graphs of

f (x) = cos (x - 30°)

and

g (x) = sin x

for the interval

x \in [- 180°; 180°]

on the same set of axes.
Clearly indicate the intersections with the axes as well as the turning points on the graph.(5)

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 6.1.2 · September 2024 · Provincial · 4 marks
6.1 Given: $f (x) = 2 sin x + 1$ and $g (x) = tan x$ , where $x \in [0^{\circ}; 27 0^{\circ}]$
6.1.2 On the same set of axes provided on the DIAGRAM SHEET, sketch the graphs of f and g. Clearly indicate all intercepts with the axes, as well as turning points and end points of the graphs.(4)
Show the memo (4 ticks)Memo
1. ✓
  Shape of fSine curve for $f (x) = 2 sin x + 1$ from $(0^{\circ}; 1)$ to $(27 0^{\circ}; - 1)$
  1 mark · Sketch a trig graph
2. ✓
  Shape of gTan curve for $g (x) = tan x$ through $(0^{\circ}; 0)$ and $(18 0^{\circ}; 0)$
  1 mark · Sketch a trig graph
3. ✓
  Asymptotes of g $x = 9 0^{\circ}$ and $x = 27 0^{\circ}$
  1 mark · Sketch a trig graph
4. ✓
  Turning point of f $(9 0^{\circ}; 3)$
  1 mark · Sketch a trig graph
4. 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
5. Question 3.2.1 · March 2022 · Provincial · 3 marks
3.2 The graph of $g (x) = - 2 cos 2 x$ for $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ is drawn below.
3.2.1 Draw the graph of $f (x) = 2 sin x - 1$ for $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ on the same set of axes with $g (x)$ .(3)
Show the memo (1 tick)Memo
1. ✓
  Sketch graph featuresTurning points: $(9 0^{\circ}; 1)$ and $(- 9 0^{\circ}; - 3)$
  Intercepts: Passes through $(3 0^{\circ}; 0)$ and $(15 0^{\circ}; 0)$ approximately
  y-intercept: $(0; - 1)$
  3 marks · Sketch a trig graph
6. Question 8.1 · March 2022 · Provincial · 6 marks
8.1 Sketch the graphs of $f (x) = sin (2 x)$ and $g (x) = 2 cos x$ for the domain $x \in [- 9 0^{\circ}; 18 0^{\circ}]$ .(6)
Show the memo (2 ticks)Memo
1. ✓
  Graph f(x)x-intercepts: $0^{\circ}, 9 0^{\circ}, 18 0^{\circ}, - 9 0^{\circ}$
  Max: $(4 5^{\circ}; 1)$
  Min: $(- 4 5^{\circ}; - 1)$
  3 marks · Sketch a trig graph
2. ✓
  Graph g(x)y-intercept: $2$
  x-intercepts: $9 0^{\circ}, - 9 0^{\circ}$
  Shape: Cosine curve
  3 marks · Sketch a trig graph

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