1 Pure Mathematics

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Question 102

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 $b$ .

[9]

1 Pure Mathematics Questions

A Level
Maths
1 Pure Mathematics

Question bank

1.1.3 Set theory language and symbols

1.1.4 Definition, domain and range of functions

A Level
Maths AQA
Question bank

1 Pure Mathematics

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Question 102

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 $b$ .

[9]

1 Pure Mathematics Questions

A Level
Maths
1 Pure Mathematics

Question bank

1.1.3 Set theory language and symbols

1.1.4 Definition, domain and range of functions