The displacement of a vibrating plate, DDD millimetres, is modelled by the function
D(t)=7sint−24cost+30,t≥0 D(t) = 7 \sin t - 24 \cos t + 30, \quad t \ge 0 D(t)=7sint−24cost+30,t≥0where ttt is the time in seconds.
Determine a sequence of transformations which maps the graph of y=sinty = \sin ty=sint onto the graph of y=D(t)y = D(t)y=D(t). Fully justify your answer.
Show that the least value of 1D(t)\frac{1}{D(t)}D(t)1 is 155\frac{1}{55}551.
Find the greatest value of 1D(t)\frac{1}{D(t)}D(t)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.