Verified answer

Since 270° < x < 360°, sin x is negative.

Since sin^2 x + cos^2 x = 1 and sin x is negative,

sin x = -sqrt(1 - cos^2 x) = -sqrt(1 - (3/29)^2) = -sqrt(832) / 29 = -8sqrt(13) / 29.

sin(2x) = 2 sin x cos x = 2(-8sqrt(13) / 29)(3/29) = -48sqrt(13) / 841.

cos(2x) = 2cos^2 x - 1 = 2(3/29)^2 - 1 = -823/841.

tan(2x) = sin(2x)/cos(2x) = [-48sqrt(13) / 841] / (-823/841) = 48sqrt(13) / 823.

Lord bless you today!