Grade 11 Maths · Trigonometry

Find solutions in an interval

List only the solutions of a trig equation that fall in a given interval, for example cos x = 0,5 for 0° ≤ x ≤ 360° gives 60° and 300°.

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General and Specific Solution grade 11: Part 2Kevinmathscience

Grade 11 Trigonometry: Trig Equations | General Solutions | Finding a specific SolutionTemdel

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Question 6.2.3 · May/June 2025 · Paper 2 · National (DBE) · 5 marks

6.2 Consider the expression:

sin (A - B) - sin (A + B)

6.2.3 Hence, determine the solution for

sin 4 x - sin 10 x = sin 3 x

for

x \in [0^{\circ}; 3 0^{\circ}]

.(5)

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More past paper questions: find solutions in an interval

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3. Question 3.4.2 · March 2025 · Provincial · 3 marks
3.4 Given: $(1 - cos^{2} x) (tan x + \frac{c o s x}{s i n x})$
3.4.2 For which value(s) of $x$ in the interval $[0^{\circ}; 36 0^{\circ})$ is the identity in QUESTION 3.4.1 undefined?(3)
Show the memo (3 ticks)Memo
1. ✓
  Correct value (1 of any 3)Undefined when $sin x = 0$ or $tan x$ is undefined: $x = 0^{\circ}$
  1 mark · Find solutions in an interval
2. ✓
  Correct value (2 of any 3) $x = 9 0^{\circ}$
  1 mark · Find solutions in an interval
3. ✓
  Correct value (3 of any 3) $x = 18 0^{\circ}$ (and $27 0^{\circ}$ ): $x \in {0^{\circ}; 9 0^{\circ}; 18 0^{\circ}; 27 0^{\circ}}$
  1 mark · Find solutions in an interval
4. Question 4.3.2 · March 2023 · Paper 1 · Provincial · 2 marks
4.3 Consider the equation: $3 cos^{2} α - sin α cos α = 0$
4.3.2 Hence, determine the values of $α$ for which $3 cos^{2} α - sin α cos α = 0$ in the interval $α \in [- 27 0^{\circ}; 9 0^{\circ}]$ .(2)
Show the memo (1 tick)Memo
1. ✓
  Substitute integer values for k to find solutions in intervalFrom $α = 9 0^{\circ} + k 18 0^{\circ}$ : $- 9 0^{\circ}; 9 0^{\circ}$ (also $- 27 0^{\circ}$ if inclusive)
  From $α = 6 0^{\circ} + k 18 0^{\circ}$ : $- 12 0^{\circ}; 6 0^{\circ}$
  2 marks · Find solutions in an interval
5. Question 7.4.2 · March 2021 · Provincial · 4 marks
7.4 Given: $f (x) = 2 cos (x - 3 0^{\circ})$
7.4.2 Use the letters P and Q to indicate on the graph the solution of the equation $cos (x - 3 0^{\circ}) = 0, 5$ and the x-coordinates of P and Q.(4)
Show the memo (1 tick)Memo
1. ✓
  Solve equation $2 cos (x - 3 0^{\circ}) = 1$ (since graph is $2 cos ...$ , looking for $y = 1$ )
  $cos (x - 3 0^{\circ}) = 0, 5$
  $x - 3 0^{\circ} = 6 0^{\circ}$ or $- 6 0^{\circ}$
  $x = 9 0^{\circ}$ or $x = - 3 0^{\circ}$
  4 marks · Find solutions in an interval
6. Question 7.2.2 · March 2024 · Paper 1 · Provincial · 3 marks
7.2 Given: $\frac{4 s i n x c o s x}{2 s i n ^{2} x - 1}$
7.2.2 For which value(s) of $x$ in the interval $- 9 0^{\circ} < x < 9 0^{\circ}$ will the above expression be undefined?(3)
Show the memo (2 ticks)Memo
1. ✓
  Set denominator to zero $2 sin^{2} x - 1 = 0$
  $sin^{2} x = \frac{1}{2}$
  $sin x = \pm \frac{1}{2}$
  1 mark · Find where trig expression is undefined
2. ✓
  Find x-values in range $x = - 4 5^{\circ}$ OR $x = 4 5^{\circ}$
  2 marks · Find solutions in an interval

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