OCR PURE 2066 — Question 3

Exam BoardOCR
ModulePURE
Year2066
TopicFactor & Remainder Theorem
TypeTrigonometric substitution equations

3 In this question you must show detailed reasoning.
  1. The polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } - 8 x + 3\).
    1. Show that \(f ( 1 ) = 0\).
    2. Solve the equation \(\mathrm { f } ( x ) = 0\).
  2. Hence solve the equation \(2 \sin ^ { 3 } \theta + 3 \sin ^ { 2 } \theta - 8 \sin \theta + 3 = 0\) for \(0 ^ { \circ } \leqslant \theta < 360 ^ { \circ }\).