Grade 10 Maths · Functions

Find trig graph amplitude and range

Find the highest and lowest values, amplitude and range of a sine or cosine graph, for example y = 3 cos x + 1 has range −2 to 4.

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Question 5.2 · 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°]

: $Diagram for this question$

5.2 Write down the range of

f

(2)

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

More past paper questions: find trig graph amplitude and range

Work each one out first, then open the memo and check every tick.

3. Question 5.3 · 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 $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
5.3 Determine the range of f.(2)
Show the memo (1 tick)Memo
1. ✓
  Determine range $y \in [0; 2]$ or $0 \leq y \leq 2$
  2 marks · Find trig graph amplitude and range
4. 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
5. Question 3.2 · 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 $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
3.2 Write down the range of $f$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Interval (min and max)Minimum $- 2$ , maximum $2$
  1 mark · Find trig graph amplitude and range
2. ✓
  Notation $- 2 \leq y \leq 2$ OR $y \in [- 2; 2]$
  1 mark · Find trig graph amplitude and range
6. Question 4.3 · June 2024 · Paper 2 · Provincial · 2 marks
Given: $f (x) = sin 2 x$ and $g (x) = 3 cos x$ for $x \in [- 9 0^{\circ}; 9 0^{\circ}]$
4.3 Write down the range of $g (x)$ .(2)
Show the memo (1 tick)Memo
1. ✓
  Determine the range based on the given domainThe maximum value is $3$ (at $x = 0^{\circ}$ ) and the minimum value on the interval $[- 9 0^{\circ}; 9 0^{\circ}]$ is $0$ (at $x = - 9 0^{\circ}$ and $x = 9 0^{\circ}$ ).
  
  $y \in [0; 3]$ or $0 \leq y \leq 3$
  2 marks · Find trig graph amplitude and range

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