How to find the value of $csc 562.5^@$ ?

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Answer 1 · 2015-06-06T01:21:03

csc 562.5 = 1/ sin 562.5

Call sin x = sin 562.5 --> cos 2x = cos 1125 deg

$cos 2x = cos 1125 = cos (45 + 3(360)) = cos 45 = sqrt2/2$

$2sin^2 x = 1 - cos 2x = 1 - sqrt2/2$ = 1 - 0.707 = 0.293

$sin^2 x = 0.146 --> sin x = 0.38$ (Quadrant I)

$csc 562.5 = 1/sin x = 1/0.38 = 2.63$

How to find the value of csc 562.5^@csc 562.5^@?