Find sin x/2, cos x/2, and tan x/2, if cos x = - 12/13, 180 degrees is less than x which is less than 270 degrees

Question

Mathematics

Landin Fuentes

21 May, 16:10

Find sin x/2, cos x/2, and tan x/2, if cos x = - 12/13, 180 degrees is less than x which is less than 270 degrees

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Answers (1)

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Emely Nixon · Answer 1

Cos x = - 12/13

sin x = - sqrt (13^2 - 12^2) / 13 = - 5/13

tan x = 5/12

tan x/2 = (1 - cos x) / sin x = 1 - (-12/13) / - 5/13 = 25/13 * - 13/5 = - 5

2sin^2 x/2 = 1 - cos x = 1 - (-12/13) = 25/13

sin^2 x/2 = 25/13 / 2 = 25/26

sin x/2 = 5/√26

sin x/2 / cos x/2 = tan x/2

cos x/2 = sin x/2 / tan x/2 = 5/√26 / - 5 = - 1/√26

sin x/2 = 5/√26

cos x/2 = - 1/√26

tan x/2 = - 5