Question

Evaluate the expression under the given conditions. cos(2); sin() = − 3 5 , in quadrant iii

Answer 1

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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