Mathematics, 17.02.2020 00:47 herbal420medici
Find the EXACT value of cos(A+B) if sinA=β8/17 where A is in Quadrant III and sec B =β5/4 where B is in Quadrant II. Assume all angles are measured from standard position. cos(A+B) =
Answers: 1
![\bf sin(A)=\cfrac{\stackrel{opposite}{-8}}{\underset{hypotenuse}{17}}\qquad \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{17^2-(-8)^2}=a\implies \pm\sqrt{225}=a\implies \pm 15 = a\implies \stackrel{III~Quadrant}{-15=a} \\\\\\ therefore\qquad \qquad cos(A)=\cfrac{-15}{17} \\\\[-0.35em] ~\dotfill](/tpl/images/0512/7988/e164b.png)
![\bf sec(B)=\cfrac{\stackrel{hypotenuse}{5}}{\underset{adjacent}{-4}}\qquad \impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \pm\sqrt{c^2-a^2}=b\implies \pm\sqrt{5^2-(-4)^2}=b\implies \pm\sqrt{9}=b \\\\\\ \pm 3 = b\implies \stackrel{II~Quadrant}{3=b}~\hfill cos(B)=\cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{5}}~\hfill sin(B)=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}} \\\\[-0.35em] ~\dotfill](/tpl/images/0512/7988/87c23.png)
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Find the EXACT value of cos(A+B) if sinA=β8/17 where A is in Quadrant III and sec B =β5/4 where B is...
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