- In a particular circuit the current, \(I\) amperes, is given by
$$I = 4 \sin \theta - 3 \cos \theta , \quad \theta > 0$$
where \(\theta\) is an angle related to the voltage.
Given that \(I = R \sin ( \theta - \alpha )\), where \(R > 0\) and \(0 \leqslant \alpha < 360 ^ { \circ }\),
- find the value of \(R\), and the value of \(\alpha\) to 1 decimal place.
- Hence solve the equation \(4 \sin \theta - 3 \cos \theta = 3\) to find the values of \(\theta\) between 0 and \(360 ^ { \circ }\).
- Write down the greatest value for \(I\).
- Find the value of \(\theta\) between 0 and \(360 ^ { \circ }\) at which the greatest value of \(I\) occurs.
8. continued