Question #143738
Suppose cos(theta) = -5/13 and tan<0 find sin(2theta)
1
Expert's answer
2020-11-11T18:59:03-0500

Cosθ=513Cos\theta=\frac{-5}{13}

Cos2θ+sin2θ=1Cos^2\theta+sin^2\theta=1

(513)2+sin2θ=1(\frac{-5}{13})^2+sin^2\theta=1

Sin2θ=125169Sin^2\theta=1-\frac{25}{169}

Sin2θ=144169Sin^2\theta=\frac{144}{169}

Sinθ=1213Sin\theta=\frac{12}{13}


Sin2θ=2sinθcosθSin2\theta=2sin\theta cos\theta

=2×1213×513=2\times \frac{12}{13} \times \frac{-5}{13}

Sin2θ=120169Sin2\theta=\frac{-120}{169}


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