OCR MEI Paper 3 2021 November — Question 13

Exam BoardOCR MEI
ModulePaper 3 (Paper 3)
Year2021
SessionNovember
TopicComplex Numbers Arithmetic
TypeArgument relationships and tangent identities

13
  1. Use triangle ABE in Fig. C 2 to show that \(\arctan x + \arctan \left( \frac { 1 } { x } \right) = \frac { \pi } { 2 }\), as given in line 29 .
  2. Sketch the graph of \(\mathrm { y } = \arctan \mathrm { x }\).
  3. What property of the arctan function ensures that \(\mathrm { y } > \frac { 1 } { \mathrm { x } } \Rightarrow \arctan y > \arctan \left( \frac { 1 } { \mathrm { x } } \right)\), as given in line 30 ?