Mathematics, 30.12.2019 05:31 mattsucre1823
Find the exact value of cot(0) for an angle 0 with sin(0)=-1/6 and with its terminal side in quadrant iii.
Answers: 2
![\bf sin(\theta )=\cfrac{\stackrel{opposite}{-1}}{\stackrel{\stackrel{never~negative}{hypotenuse}}{6}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{6^2-(-1)^2}=a\implies \pm\sqrt{35}=a\implies \stackrel{III~Quadrant}{-\sqrt{35}=a} \\\\[-0.35em] ~\dotfill](/tpl/images/0437/0188/7351b.png)
![\bf \pm\sqrt{6^2-(-1)^2}=a\implies \pm\sqrt{35}=a\implies \stackrel{III~Quadrant}{-\sqrt{35}=a} \\\\[-0.35em] ~\dotfill\\\\ cot(\theta )=\cfrac{\stackrel{adjacent}{-\sqrt{35}}}{\stackrel{opposite}{-1}}\implies cot(\theta )=\sqrt{35}](/tpl/images/0437/0188/408cc.png)
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Find the exact value of cot(0) for an angle 0 with sin(0)=-1/6 and with its terminal side in quadran...
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