The potential difference VVV, in millivolts, across a resistor in an alternating current circuit is modeled by the function V(t)=7cost−24sintV(t) = 7\cos t - 24\sin tV(t)=7cost−24sint, where t t\,t is the time in milliseconds since the circuit was closed.
Express V(t)V(t)V(t) in the form Rcos(t+α)R\cos(t + \alpha)Rcos(t+α), where R>0 R > 0\,R>0 and 0<α<π2\displaystyle 0 < \alpha < \frac{\pi}{2}0<α<2π. Give the exact value of R R\,R and the value of α\alphaα, in radians, to 3 decimal places.
The curve with equation y=costy = \cos ty=cost is transformed onto the curve with equation y=V(t)y = V(t)y=V(t) by a sequence of two transformations.
Given that the first transformation is a stretch and the second is a translation:
(i) Describe fully the transformation that is a stretch. (ii) Describe fully the transformation that is a translation.
The power efficiency G G\,G of a specific component is given by G(t)=210075+(V(t))2\displaystyle G(t) = \frac{2100}{75 + (V(t))^2}G(t)=75+(V(t))22100. Find the range of GGG.
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.