Simple double angle equations (direct substitution)

Equations where sin2x, cos2x, or tan2x appears alone or with a constant, solved by direct substitution of the double angle (e.g. sin2x = 0.7, tan2x = 3, sin2x = -0.5). No mixing with single-angle terms.

14 questions · Moderate -0.6

1.05o Trigonometric equations: solve in given intervals
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CAIE P1 2012 June Q1
4 marks Moderate -0.3
1 Solve the equation \(\sin 2 x = 2 \cos 2 x\), for \(0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }\).
OCR MEI C2 Q4
3 marks Moderate -0.8
4 Solve the equation \(\tan 2 \theta = 3\) for \(0 ^ { \circ } < \theta < 360 ^ { \circ }\).
[0pt] [3]
OCR MEI C2 Q5
5 marks Moderate -0.3
5 Solve the equation \(\sin 2 \theta = 0.7\) for values of \(\theta\) between 0 and \(2 \pi\), giving your answers in radians correct to 3 significant figures.
OCR MEI C2 Q6
3 marks Moderate -0.8
6 Solve the equation \(\sin 2 x = - 0.5\) for \(0 ^ { \circ } < x < 180 ^ { \circ }\).
OCR MEI C2 2009 January Q4
3 marks Moderate -0.8
4 Solve the equation \(\sin 2 x = - 0.5\) for \(0 ^ { \circ } < x < 180 ^ { \circ }\).
OCR MEI C2 2012 June Q8
5 marks Moderate -0.8
8 Solve the equation \(\sin 2 \theta = 0.7\) for values of \(\theta\) between 0 and \(2 \pi\), giving your answers in radians correct to 3 significant figures.
OCR MEI Paper 3 2021 November Q2
2 marks Moderate -0.8
2 Solve the equation \(\sin 2 x = 0.3\) for \(0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }\). Give your answer(s) correct to \(\mathbf { 1 }\) decimal place.
CAIE P1 2012 June Q4
6 marks Moderate -0.8
  1. Solve the equation \(\sin 2x + 3 \cos 2x = 0\) for \(0° \leqslant x \leqslant 360°\). [5]
  2. How many solutions has the equation \(\sin 2x + 3 \cos 2x = 0\) for \(0° \leqslant x \leqslant 1080°\)? [1]
Edexcel C2 Q6
6 marks Moderate -0.3
Given that \(2 \sin 2\theta = \cos 2\theta\),
  1. show that \(\tan 2\theta = 0.5\). [1]
  2. Hence find the values of \(\theta\), to one decimal place, in the interval \(0 \leq \theta < 360\) for which \(2 \sin 2\theta ° = \cos 2\theta °\). [5]
Edexcel C2 Q3
6 marks Moderate -0.8
Given that \(2 \sin 2\theta = \cos 2\theta\),
  1. show that \(\tan 2\theta = 0.5\). [1]
  2. Hence find the values of \(\theta\), to one decimal place, in the interval \(0 \leq \theta < 360\) for which \(2 \sin 2\theta° = \cos 2\theta°\). [5]
Edexcel C2 Q2
6 marks Moderate -0.3
Given that \(2 \sin 2\theta = \cos 2\theta\),
  1. show that \(\tan 2\theta = 0.5\). [1]
  2. Hence find the values of \(\theta\), to one decimal place, in the interval \(0 \leq \theta < 360\) for which \(2 \sin 2\theta° = \cos 2\theta°\). [5]
OCR MEI C2 2014 June Q9
3 marks Moderate -0.3
Solve the equation \(\tan 2\theta = 3\) for \(0° < \theta < 360°\). [3]
OCR MEI C4 2012 January Q2
4 marks Moderate -0.3
Solve, correct to 2 decimal places, the equation \(\cot 2\theta = 3\) for \(0° < \theta < 180°\). [4]
WJEC Unit 1 2024 June Q2
3 marks Moderate -0.8
Find all values of \(\theta\) in the range \(0° < \theta < 180°\) that satisfy the equation $$2\sin 2\theta = 1.$$ [3]