Question

Given θ is in the third quadrant, φ is in the second quadrant, sinθ=-5/13, and tanφ=-8/15. Find the value of tan(π+θ)1) 12/52) 13) 5/12

Answer 1

$\begin{gathered} \sin \theta=\frac{-5}{13} \\ \tan (\pi+\theta)=\tan \theta \\ \sin \theta=\frac{p}{h} \\ \text{base}=\sqrt[]{(hypotonous)^2-(perpendicular)^2} \\ =\sqrt[]{(13)^2-(-5)}^2 \\ =\sqrt[]{169-25} \\ =\sqrt[]{144} \\ =12 \\ \tan \theta=\frac{p}{b} \\ \tan \theta=\frac{-5}{12} \end{gathered}$