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.
