The voltage VVV (in volts) in an alternating current circuit is modeled by the function V(t)=asint+bcostV(t) = a \sin t + b \cos tV(t)=asint+bcost, where t t\,t is the time in seconds and a,b a, b\,a,b are constants.
The peak voltage of the circuit is 10 V. At time t=π3\displaystyle t = \frac{\pi}{3}t=3π, the voltage is exactly -5 V. It is known that at this instant, the voltage is decreasing.
Given that the initial voltage at t=0t = 0t=0 is positive, determine the exact values of a a\,a and bbb.
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.