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 (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.