![\bf sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a\implies \stackrel{III~Quadrant}{-12=a} \\\\[-0.35em] ~\dotfill](/tpl/images/0056/2496/98b0f.png)
![\bf tan(\theta )\implies \cfrac{sin(\theta )}{cos(\theta )}\implies \cfrac{~~-\frac{5}{13}~~}{-\frac{12}{13}}\implies -\cfrac{5}{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\times -\cfrac{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{12}\implies \cfrac{5}{12} \\\\[-0.35em] ~\dotfill](/tpl/images/0056/2496/7f619.png)
Find the value of tan( π + θ) if θ terminates in quadrant iii and sinθ = -5/13.
-5/13
-5...
Mathematics, 06.07.2019 02:10 cfonse11
Find the value of tan( π + θ) if θ terminates in quadrant iii and sinθ = -5/13.
-5/13
-5/12
0
5/12
Answers: 1
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