A deep-space communication laser's alignment angle ψ \psi\,ψ is modeled by the equation
6sinψcosψcosψ+sinψ=(5+sec2ψ)(cosψ−sinψ) \frac{6 \sin \psi \cos \psi}{\cos \psi + \sin \psi} = (5 + \sec 2\psi)(\cos \psi - \sin \psi) cosψ+sinψ6sinψcosψ=(5+sec2ψ)(cosψ−sinψ)Show that this equation can be simplified to the form
6sin2ψ−10cos2ψ=2 6 \sin 2\psi - 10 \cos 2\psi = 2 6sin2ψ−10cos2ψ=2For an observation window 0<t<π0 < t < \pi0<t<π, determine the values of the signal time t t\,t satisfying
6sintcostcost+sint=(5+sec2t)(cost−sint) \frac{6 \sin t \cos t}{\cos t + \sin t} = (5 + \sec 2t)(\cos t - \sin t) cost+sint6sintcost=(5+sec2t)(cost−sint)giving your answers to 3 significant figures.
317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.