I have no idea how to do this, can some one explain to me step by step?

Start out by letting x = arcsin(5/13) so that sin(x) = 5/13. Then, we wish to find:

cos[2arcsin(5/13)] = cos(2x).

Using the double-angle formula for cosine, we have:

cos(2x) = 1 – 2sin^2(x)

= 1 – 2(5/13)^2, since sin(x) = 5/13

= 119/169.

And, no, Patrick, re-writing 0.7034 as 9.144/13 does not make your answer any more exact.

cos(2sin^-1(5/13))

start by simplifying sin^-1(5/13)

theta = (sin^-1(x))

x = sin(theta)

5/13 = sin (theta)

solve for theta:

theta = (sin^-1(5/13)) = 22.62

cos(2*22.62) = .704

cos(2*22.65) = cos(45.3) = 0.7034 =9.144/13

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