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.
348 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.