The equation asin2θ=cosθ+ba\sin^2\theta=\cos\theta+basin2θ=cosθ+b, where a a\,a and b b\,b are constants, has solutions satisfying cosθ=0.5\cos\theta=0.5cosθ=0.5 and cosθ=−23\displaystyle \cos\theta=-\frac{2}{3}cosθ=−32.
Find the values of a a\,a and bbb.
Hence, solve asin22θ=cos2θ+ba\sin^2 2\theta=\cos 2\theta+basin22θ=cos2θ+b giving all the solutions for the interval 0≤θ<360∘ 0\leq\theta<360^\circ\,0≤θ<360∘
Give non-integer answers to one decimal place.
322 exam-style questions on Edexcel A Level Maths Trigonometric Identities and Equations, covering 10.1 Angles in all four Quadrants, 10.2 Exact Values of Trigonometric Ratios, 10.3 Trigonometric Identities, 10.4 Solving Trigonometric Equations, 10.5 Harder Trigonometric Equations, and 10.6 Equations and Identities. Each one has a worked solution and a mark scheme showing where the marks go.