5. (a) Prove that, when \(x = \frac { 1 } { 15 }\), the value of \(( 1 + 5 x ) ^ { - \frac { 1 } { 2 } }\) is exactly equal to \(\sin 60 ^ { \circ }\).
(3)
(b) Expand \(( 1 + 5 x ) ^ { - \frac { 1 } { 2 } } , | x | < 0.2\), in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), simplifying each term.
(c) Use your answer to part (b) to find an approximation for \(\sin 60 ^ { \circ }\).
(d) Find the difference between the exact value of \(\sin 60 ^ { \circ }\) and the approximation in part (c).