Show that 5cos2t−5cos6t≈80t25\cos 2t - 5\cos 6t \approx 80t^25cos2t−5cos6t≈80t2 for small values of ttt.
The output signal of a high-frequency sensor is modeled by the function R(t)=120(5cos2t−5cos6t)R(t) = \sqrt{\frac{1}{20}(5\cos 2t - 5\cos 6t)}R(t)=201(5cos2t−5cos6t). Show that for small positive values of ttt, the area enclosed by the curve y=R(t)y = R(t)y=R(t), the ttt-axis, and the line t=0.4t = 0.4t=0.4 can be approximated by Area≈2m×5n\text{Area} \approx 2^m \times 5^nArea≈2m×5n where mmm and nnn are integers to be found.
Explain why ∫12.612.72t dt\int_{12.6}^{12.7} 2t \, dt∫12.612.72tdt is not a suitable approximation for ∫12.612.7R(t) dt\int_{12.6}^{12.7} R(t) \, dt∫12.612.7R(t)dt.
Explain how ∫12.612.7R(t) dt\int_{12.6}^{12.7} R(t) \, dt∫12.612.7R(t)dt may be approximated by ∫ab2t dt\int_{a}^{b} 2t \, dt∫ab2tdt for suitable values of aaa and bbb.
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.