4400 Higher November 2005 Paper 4 Q17
17 Three functions are defined as follows:
\(\mathrm{f} : x \mapsto \cos x^\circ\) for the domain \(0 \leqslant x \leqslant 180\)
\(\mathrm{g} : x \mapsto \sin x^\circ\) for the domain \(0 \leqslant x \leqslant 90\)
\(\mathrm{h} : x \mapsto \tan x^\circ\) for the domain \(p \leqslant x \leqslant q\)
(a) Find the range of \(\mathrm{f}\). (2)
(b) Given that the range of \(\mathrm{h}\) is the same as the range of \(\mathrm{g}\), find a value of \(p\) and a value of \(q\). (3)
| Scheme | Marks |
|---|---|
| \(-1 \leqslant \mathrm{f}(x) \leqslant 1\) | B1 B1 |
| (2) |
Notes
B1B1: or −1 to 1 oe
| Scheme | Marks |
|---|---|
| range of g : 0 to 1 | |
| \(p = 0,\ q = 45\) | B3 |
| (3) | |
| (5 marks) |
Notes
B3: both correct : B3
g : 0 to 1 & one end correct : B2
g : 0 to 1 or one end correct : B1