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

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Jun 8, 2015

Call #tan x = t = 7/24#. Use the trig identity:# cos 2x = (1 - t^2)/(1 + t^2)#

#cos 2x = (1 - 49/576)/(1 + 49/576) = 527/625 = 0.84#

#cos 2x = 0.84 -> 2x = +- 32.50 deg#

Since x lies in Quadrant III, then we choose cos 2x = cos (32.50 + 360) = 0.84.

Note:# x = (360 + 32.50)/2 = 196.25 # deg (Q. III)

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