AQA C4 2008 June — Question 5

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2008
SessionJune
TopicAddition & Double Angle Formulae
5
  1. The angle \(\alpha\) is acute and \(\sin \alpha = \frac { 4 } { 5 }\).
    1. Find the value of \(\cos \alpha\).
    2. Express \(\cos ( \alpha - \beta )\) in terms of \(\sin \beta\) and \(\cos \beta\).
    3. Given also that the angle \(\beta\) is acute and \(\cos \beta = \frac { 5 } { 13 }\), find the exact value of \(\cos ( \alpha - \beta )\).
    1. Given that \(\tan 2 x = 1\), show that \(\tan ^ { 2 } x + 2 \tan x - 1 = 0\).
    2. Hence, given that \(\tan 45 ^ { \circ } = 1\), show that \(\tan 22 \frac { 1 } { 2 } ^ { \circ } = \sqrt { 2 } - 1\).
This paper (8 questions)
View full paper
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8