The voltage $V$ (in volts) in an alternating current circuit is modeled by the function $\sin t + b \cos t$ , where $t\,$ is the time in seconds and $b\,$ are constants.

The peak voltage of the circuit is 10 V. At time $t=π3\displaystyle t = \frac{\pi}{3}$ , the voltage is exactly -5 V. It is known that at this instant, the voltage is decreasing.

Given that the initial voltage at $t = 0$ is positive, determine the exact values of $a\,$ and $b$ .

The voltage $V$ (in volts) in an alternating current circuit is modeled by the function $\sin t + b \cos t$ , where $t\,$ is the time in seconds and $b\,$ are constants.

The peak voltage of the circuit is 10 V. At time $t=π3\displaystyle t = \frac{\pi}{3}$ , the voltage is exactly -5 V. It is known that at this instant, the voltage is decreasing.

Given that the initial voltage at $t = 0$ is positive, determine the exact values of $a\,$ and $b$ .

3 Unit A2 1: Pure Mathematics (A-level only)

Question 253

Markscheme

3 Unit A2 1: Pure Mathematics (A-level only)

Question 253

Markscheme

3 Unit A2 1: Pure Mathematics (A-level only)

Question 253

3 Unit A2 1: Pure Mathematics (A-level only) Questions

3 Unit A2 1: Pure Mathematics (A-level only)

Question 253

3 Unit A2 1: Pure Mathematics (A-level only) Questions