It is given that
(sinθ+6cosθ)2+(3sinθ−2cosθ)2=28(\sin\theta + 6\cos\theta)^2 + (3\sin\theta - 2\cos\theta)^2 = 28(sinθ+6cosθ)2+(3sinθ−2cosθ)2=28
and that θ \theta\,θ is obtuse.
Find the exact value of sinθ\sin\thetasinθ. Fully justify your answer.
Find the exact value of cos2θ\cos 2\thetacos2θ.
Find the exact value of tanθ\tan\thetatanθ, giving your answer in surd form.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.