Grade 11 Maths · Trigonometry

Use a reduction formula

Rewrite trig ratios of big or negative angles using an acute angle and the right sign, for example sin(180° + x) = −sin x.

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Grade 11 Trigonometry Reduction IntroductionMiss Martins Maths and Science

Grade 11 Trigonometry Reduction with Negative AnglesMiss Martins Maths and Science

Reduction Grade 11: ExamKevinmathscience

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Question 7.5 · May/June 2025 · Paper 2 · National (DBE) · 2 marks

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}]

7.5 Graph g is shifted

4 5^{\circ}

to the right to obtain a new graph h.

Determine the equation of h in its simplest form.(2)

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

More past paper questions: use a reduction formula

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

3. Question 5.3.1 · November 2024 · Paper 2 · Provincial · 2 marks
5.3 If $cos 42° = p$ :

Determine the following in terms of $p$ :
5.3.1 $cos 138°$ (2)
Show the memo (2 ticks)Memo
1. ✓
  $- cos 42°$ $cos 138°$
  $= - cos 42°$
  1 mark · Use a reduction formula
2. ✓
  Answer $= - p$
  1 mark · Use a reduction formula
4. Question 2.1.1 · June 2024 · Paper 2 · Provincial · 2 marks
2.1 Given: $sin 2 0^{\circ} = p$ . Determine the following in terms of $p$ :
2.1.1 $sin (- 2 0^{\circ})$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Negative angle rule $sin (- 2 0^{\circ}) = - sin 2 0^{\circ}$
  1 mark · Use a reduction formula
2. ✓
  Answer in terms of p $= - p$
  1 mark · Use a reduction formula
5. Question 7.1.3 · March 2023 · Provincial · 3 marks
7.1 Given $cos 4 0^{\circ} = t$ .

Without using a calculator, determine each of the following in terms of t.
7.1.3 $cos 22 0^{\circ}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Write as cos(180° + 40°) $cos 22 0^{\circ} = cos (18 0^{\circ} + 4 0^{\circ})$
  1 mark · Use a reduction formula
2. ✓
  Reduce to -cos 40° $= - cos 4 0^{\circ}$
  1 mark · Use a reduction formula
3. ✓
  Answer in terms of t $= - t$
  1 mark · Use a reduction formula
6. Question 3.3.1 · March 2019 · Provincial · 2 marks
3.3 Determine the value of the following in terms of p, if $cos 3 2^{\circ} = p$
3.3.1 $cos 21 2^{\circ}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Reduction $cos (18 0^{\circ} + 3 2^{\circ}) = - cos 3 2^{\circ}$
  1 mark · Use a reduction formula
2. ✓
  Substitution $- p$
  1 mark · Use a reduction formula

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