Quartic in sin or cos substitution

A question is this type if and only if the equation involves sin⁴θ or cos⁴θ (or tan²θ in terms of a squared substitution) requiring a substitution u=sin²θ or u=cos²θ to produce a quadratic in u.

4 questions · Moderate -0.1

1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals
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CAIE P1 2020 November Q3
5 marks Standard +0.3
3 Solve the equation \(3 \tan ^ { 2 } \theta + 1 = \frac { 2 } { \tan ^ { 2 } \theta }\) for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).
CAIE P1 2011 June Q5
6 marks Moderate -0.3
5
  1. Show that the equation \(2 \tan ^ { 2 } \theta \sin ^ { 2 } \theta = 1\) can be written in the form $$2 \sin ^ { 4 } \theta + \sin ^ { 2 } \theta - 1 = 0 .$$
  2. Hence solve the equation \(2 \tan ^ { 2 } \theta \sin ^ { 2 } \theta = 1\) for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).
CAIE P1 2003 November Q2
5 marks Moderate -0.3
2
  1. Show that the equation \(4 \sin ^ { 4 } \theta + 5 = 7 \cos ^ { 2 } \theta\) may be written in the form \(4 x ^ { 2 } + 7 x - 2 = 0\), where \(x = \sin ^ { 2 } \theta\).
  2. Hence solve the equation \(4 \sin ^ { 4 } \theta + 5 = 7 \cos ^ { 2 } \theta\), for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).
CAIE P1 2024 November Q4
4 marks Moderate -0.3
Solve the equation \(4\sin^4\theta + 12\sin^2\theta - 7 = 0\) for \(0° \leqslant \theta \leqslant 360°\). [4]