Question

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

Answer 1

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`