How do you determine an exact value for cos(2x) when angle x lies in 3rd quadrant and tanx=7/24

Bellenik3

Bellenik3

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2022-08-21

How do you determine an exact value for cos ( 2 x ) when angle x lies in 3rd quadrant and tan x = 7 24 ?

Answer & Explanation

Mohammad Orr

Mohammad Orr

Beginner2022-08-22Added 8 answers

Call tan x = t = 7 24 . Use the trig identity: cos 2 x = 1 t 2 1 + t 2
cos 2 x = 1 49 576 1 + 49 576 = 527 625 = 0.84
cos 2 x = 0.84 2 x = ± 32.50 d e g
Since x lies in Quadrant III, then we choose cos 2 x = cos ( 32.50 + 360 ) = 0.84.
Note: x = 360 + 32.50 2 = 196.25 deg (Q. III)

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