Grade 10 Maths · Trigonometry · Find trig graph amplitude and range

Amplitude of Trig Graphs Grade 10

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

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Question 6.2 · November 2023 · Paper 2 · National (DBE) · 2 marks

In the diagram, the graphs of

f (x) = 2 sin 2 x

and

g (x) = - cos (x + 45°)

are drawn for the interval

x \in [0°; 180°]

A (105°; - 1)

lies on

f

. $Diagram for this question$

6.2 Determine the range of

g

in the interval

x \in [0°; 180°]

.(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

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3. Question 5.2.3 · November 2023 · Paper 2 · National (DBE) · 2 marks
5.2 Given: $\frac{c o s ^{4} x + s i n ^{2} x . c o s ^{2} x}{1 + s i n x}$
5.2.3 Write down the minimum value of the function defined by $y = \frac{c o s ^{4} x + s i n ^{2} x . c o s ^{2} x}{1 + s i n x}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Minimum = 0 $y = \frac{c o s ^{4} x + s i n ^{2} x . c o s ^{2} x}{1 + s i n x}$
  $y = 1 - sin x$
  $∴$ Minimum $= 0$
  2 marks · Find trig graph amplitude and range
4. Question 6.3 · November 2022 · Paper 2 · National (DBE) · 2 marks
In the diagram below, the graphs of $f (x) = tan x$ and $g (x) = 2 sin 2 x$ are drawn for the interval $x \in [- 180°; 180°]$ . $A (60°; k)$ and B are two points of intersection of $f$ and $g$ . $Diagram for this question$
6.3 Write down the range of $2 g (x)$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  $y \in [- 2; 2]$ Range of $g$ : $y \in [- 2; 2]$
  1 mark · Find trig graph amplitude and range
2. ✓
  AnswerRange of $2 g (x)$ : $y \in [- 4; 4]$
  1 mark · Find trig graph amplitude and range
5. Question 6.1 · November 2018 · Paper 2 · National (DBE) · 2 marks
The graphs of the functions $f (x) = a cos b θ$ and $g (x) = c tan θ$ for $x \in [- 180°; 180°]$ are sketched below. The graphs intersect at P $(58°; 1, 6)$ and Q. $Diagram for this question$
6.1 Write down the range of $f$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  End points $- 3$ and $3$
  1 mark · Find trig graph amplitude and range
2. ✓
  Notation $- 3 \leq y \leq 3$ or $y \in [- 3; 3]$
  1 mark · Find trig graph amplitude and range
6. Question 6.2.2 · November 2017 · Paper 2 · National (DBE) · 2 marks
6.2 Consider the functions $f (x) = sin (x - 30°)$ and $g (x) = cos 2 x$
6.2.2 State the range of $f$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Values $- 1$ and $1$
  1 mark · Find trig graph amplitude and range
2. ✓
  Notation $- 1 \leq y \leq 1$ OR $y \in [- 1; 1]$
  1 mark · Find trig graph amplitude and range

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