OCR MEI C4 — Question 6

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
TopicHarmonic Form

6 The function \(\mathrm { f } ( \theta ) = 3 \sin \theta + 4 \cos \theta\) is to be expressed in the form \(r \sin ( \theta + \alpha )\) where \(r > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\).
  1. Find the values of \(r\) and \(\alpha\).
  2. Write down the maximum and minimum value of \(\mathrm { f } ( \theta )\).
  3. Solve the equation \(\mathrm { f } ( \theta ) = 1\) for \(0 ^ { \circ } \leq \theta \leq 180 ^ { \circ }\).