Grade 10 Maths · Trigonometry · Find equation of a trig graph

Equation of a Trig Graph Grade 10

Read the numbers in a trig graph's equation from its picture, for example a graph with amplitude 2 and period 180^ is y = 2 2x.

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Question 6.3 · November 2019 · Paper 2 · National (DBE) · 2 marks

Sketched below are the graphs of the functions

f (x) = cos x + q

and

g (x) = 2 sin b x

for

x \in [- 60°; 120°]

. $Diagram for this question$

6.3 Determine the values of

q

and

b

.(2)

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

More past paper questions: find equation of a trig graph

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3. Question 7.1 · September 2026 · Paper 2 · Provincial · 2 marks
Given: $f (x) = a cos (x + p)$ where $x \in [- 180°; 180°]$ $Diagram for this question$
7.1 Determine the values of $a$ and $p$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Value of $a$ $a = 1$
  1 mark · Find equation of a trig graph
2. ✓
  Value of $p$ $p = 30°$
  1 mark · Find equation of a trig graph
4. Question 5.1 · November 2025 · Paper 2 · Provincial · 2 marks
Given: $f (x) = a sin (\frac{x}{2}) - 1$ and $g (x) = cos x + q$ , $x \in [- 90°; 270°]$

The graphs of $f$ and $g$ are drawn below.

Use the graphs to answer the following questions where $x \in [- 90°; 270°]$ : $Diagram for this question$
5.1 Determine the values of $a$ and $q$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Value of $a$ $a = 1$
  1 mark · Find equation of a trig graph
2. ✓
  Value of $q$ $q = 0$
  1 mark · Find equation of a trig graph
5. Question 5.1 · November 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, the graphs of $f (x) = cos x + a$ and $g (x) = b sin x$ are drawn for $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
5.1 Write down the values of a and b.(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify shifts/stretches $a = 1$ (vertical shift)
  $b = - 2$ (reflection and amplitude)
  2 marks · Find equation of a trig graph
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

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