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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