The function f f\,f is defined by
f(x)=2arcsin(x−1)f(x) = 2\arcsin(x - 1)f(x)=2arcsin(x−1)
where f f\,f has its greatest possible domain.
Using set notation, state the domain of fff.
Using set notation, state the range of fff.
Find the exact value of f(1.5)f(1.5)f(1.5).
State the coordinates of the endpoint of the graph of y=f(x)y = f(x)y=f(x) at which both x x\,x and f(x)f(x)f(x) take their greatest values.
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.