Grade 10 Maths · Trigonometry · State period of a trig graph

Period of Trig Graphs Grade 10

Find how many degrees a trig graph takes to repeat itself, for example y = 2x has a period of 360^ 2 = 180^.

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Question 8.2 · September 2026 · Paper 2 · Provincial · 2 marks

The diagram below shows the graph of

f (x) = sin a x

for

x \in [- 90°; 90°]

and

y = \frac{1}{2}

. $Diagram for this question$

8.2 Write down the period of

f (\frac{3 x}{2})

.(2)

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

More past paper questions: state period of a trig graph

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3. Question 7.1 · November 2025 · Paper 2 · National (DBE) · 1 mark
In the diagram, the graph of $f (x) = cos 2 x$ is drawn for $x \in [- 135°; 135°]$ . $Diagram for this question$
7.1 Write down the period of $f$ .(1)
Show the memo (1 tick)Memo
1. ✓
  Answer $180°$
  1 mark · State period of a trig graph
4. Question 7.2 · May/June 2025 · Paper 2 · National (DBE) · 1 mark
In the diagram, the graphs of $f (x) = 2 cos x + 1$ and $g (x) = sin 2 x$ are drawn for the interval $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
7.2 Write down the period of g.(1)
Show the memo (1 tick)Memo
1. ✓
  State the period $18 0^{\circ}$
  1 mark · State period of a trig graph
5. Question 7.3.1 · November 2024 · Paper 2 · National (DBE) · 1 mark
In the diagram below, the graph of $f (x) = tan x$ is drawn for the interval $x \in [- 180°; 180°]$ . $Diagram for this question$
7.3 Given: $g (x) = cos 2 x + 1$
7.3.1 Write down the period of $g$ .(1)
Show the memo (1 tick)Memo
1. ✓
  Answer $180°$
  1 mark · State period of a trig graph
6. Question 6.1 · May/June 2024 · Paper 2 · National (DBE) · 1 mark
In the diagram, the graphs of $f (x) = cos (x + a)$ and $g (x) = sin 2 x$ are drawn for the interval $x \in [- 180°; 180°]$ . The graphs intersect at $N (- 75°; k)$ , $P (45°; 1)$ and $Q (165°; k)$ . P is also a turning point of both graphs. $Diagram for this question$
6.1 Write down the period of $f$ .(1)
Show the memo (1 tick)Memo
1. ✓
  360°Period $= 360°$
  1 mark · State period of a trig graph

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