The function f f\,f is defined by f(x)=arctanxf(x) = \arctan xf(x)=arctanx for x∈Rx \in \mathbb{R}x∈R.
Sketch the graph of y=f(x)y = f(x)y=f(x), stating the equations of its asymptotes.
Using set notation, state the range of fff.
The function g g\,g is defined by g(x)=arccosxg(x) = \arccos xg(x)=arccosx, where g g\,g has its greatest possible domain.
Using set notation, state the domain and the range of ggg.
Show that arccosx+arcsinx=π2\displaystyle \arccos x + \arcsin x = \frac{\pi}{2}arccosx+arcsinx=2π for −1≤x≤1-1 \leq x \leq 1−1≤x≤1.
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.