The value of a particular trigonometric expression that is cos 2θ under the third quadrant is -119/169
Given:
sin θ = -⁵/₁₃
This can be seen from the trigonometric identity.
cos 2θ = 1 - 2sin²θ
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;
cos 2θ = -119/169
so; cos θ is negative in the third quadrant, so ;
cos 2θ = -119/169
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