Connect the curve 5

Calculus Level 2

The curve of \(\sin { \left( ax \right) } \) is tangent to the curve of \(\sin { \left( x \right) } \) at \(x=\frac { 5\pi }{2 } \).

If minimum positive value of \(a\) can be expressed as \(\frac { A }{B }\) for co-prime \(A\) and \(B\), then find \(A+B\).

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