Grade 10 Maths · Functions

Find equation of a trig graph

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 sin 2x.

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Trig functions grade 11 and 12: Determine EquationKevinmathscience

Trigonometric Functions Grade 10 | Finding the Equation of Sin & Cos GraphGridwell Maths Tutoring

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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)

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 8.1 · March 2024 · Paper 1 · Provincial · 2 marks
In the diagram below, the graphs of $f (x) = cos x + m$ and $g (x) = sin (x + n)$ are drawn on the same set of axes for $x \in [- 24 0^{\circ}; 24 0^{\circ}]$ . $A$ is an $x$ -intercept of $f$ and has coordinates $(6 0^{\circ}; 0)$ . $B$ is a turning point of $g$ and has coordinates $(6 0^{\circ}; 1)$ .
8.1 Determine the values of $m$ and $n$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Calculate m using point A $0 = cos 6 0^{\circ} + m$
  $0 = 0, 5 + m$
  $m = - 0, 5$
  1 mark · Find equation of a trig graph
2. ✓
  Calculate n using point B $1 = sin (6 0^{\circ} + n)$
  $6 0^{\circ} + n = 9 0^{\circ}$
  $n = 3 0^{\circ}$
  1 mark · Find equation of a trig graph
4. 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
5. Question 9.1 · March 2023 · Provincial · 2 marks
In the diagram below, the graphs of $f (x) = sin a x$ and $g (x) = cos (x + b)$ are drawn for the interval $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ . Points given: $A (4 5^{\circ}; 1)$ , $B (16 5^{\circ}; - \frac{1}{2})$ .
9.1 Determine the values of $a$ and $b$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Determine aPeriod of f is $18 0^{\circ}$ . $a = \frac{360}{180} = 2$ .
  1 mark · Find equation of a trig graph
2. ✓
  Determine bMax of standard cosine is at 0. Here max is at $4 5^{\circ}$ (point A). Shift is $4 5^{\circ}$ right. $b = - 4 5^{\circ}$ .
  1 mark · Find equation of a trig graph

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