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.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
