The value of the given trigonometric expression which is cos 2θ under the 3rd quadrant is; -119/169
We are given the trigonometric ratio;
sin θ = -⁵/₁₃
From trigonometric identities, we know that;
cos 2θ = 1 - 2sin²θ
Thus;
cos 2θ = 1 - 2(-⁵/₁₃)²
cos 2θ = 1 - 2(25/169)
cos 2θ = 119/169
since cos θ is negative in the third quadrant, then we have;l
cos 2θ = -119/169
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