Grade 10 Maths · Functions

State period of a trig graph

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

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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)

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More past paper questions: state period of a trig graph

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3. Question 4.3.2 · November 2025 · Paper 2 · Provincial · 1 mark
4.3 Given: $\frac{c o s x . t a n x}{2 [ s i n x . c o s ( x - 90° ) + c o s x . c o s ( - x ) ]}$
4.3.2 Hence, or otherwise, write down the period of the expression in QUESTION 4.3(1)
Show the memo (1 tick)Memo
1. ✓
  AnswerPeriod $= 360°$
  1 mark · State period of a trig graph
4. Question 6.2.1 · March 2025 · Provincial · 1 mark
6.2 In the diagram, the graphs of $f (x) = sin 2 x$ and $g (x) = cos (x - 4 5^{\circ})$ are drawn for the interval $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
6.2.1 Write down the period of $g$ .(1)
Show the memo (1 tick)Memo
1. ✓
  State period $36 0^{\circ}$
  1 mark · State period of a trig graph
5. Question 8.3 · March 2024 · Paper 1 · Provincial · 1 mark
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 $(6 0^{\circ}; 1)$ .
8.3 If $h (x) = g (2 x)$ , write down the period of $h$ .(1)
Show the memo (1 tick)Memo
1. ✓
  Calculate period for compressed functionPeriod $= \frac{36 0 ^{\circ}}{2} = 18 0^{\circ}$
  1 mark · State period of a trig graph
6. Question 6.1 · November 2024 · Paper 2 · Provincial · 1 mark
The graph of $f (x) = cos (x + 30°)$ in the interval of $x \in [- 120°; 150°]$ has been drawn in the diagram below. $Diagram for this question$
6.1 Write down the period of $f$ .(1)
Show the memo (1 tick)Memo
1. ✓
  AnswerPeriod is $360°$
  1 mark · State period of a trig graph

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