| Date | November 2016 | Marks available | 2 | Reference code | 16N.1.sl.TZ0.2 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
Let \(\sin \theta = \frac{{\sqrt 5 }}{3}\), where \(\theta \) is acute.
Find \(\cos \theta \).
[3]
a.
Find \(\cos 2\theta \).
[2]
b.
Markscheme
evidence of valid approach (M1)
eg\(\,\,\,\,\,\)right triangle, \({\cos ^2}\theta = 1 - {\sin ^2}\theta \)
correct working (A1)
eg\(\,\,\,\,\,\)missing side is 2, \(\sqrt {1 - {{\left( {\frac{{\sqrt 5 }}{3}} \right)}^2}} \)
\(\cos \theta = \frac{2}{3}\) A1 N2
[3 marks]
a.
correct substitution into formula for \(\cos 2\theta \) (A1)
eg\(\,\,\,\,\,\)\(2 \times {\left( {\frac{2}{3}} \right)^2} - 1,{\text{ }}1 - 2{\left( {\frac{{\sqrt 5 }}{3}} \right)^2},{\text{ }}{\left( {\frac{2}{3}} \right)^2} - {\left( {\frac{{\sqrt 5 }}{3}} \right)^2}\)
\(\cos 2\theta = - \frac{1}{9}\) A1 N2
[2 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
