Question

O valor da expressão

[ sen 8pi/3 −cos 2pi]
Tg 13pi/6


é:




URGENTE

Answer 1

Expressão Trigonométrica

$\large \boxed{ \boxed{ \large \sf \dfrac{sen \dfrac{8 \pi}{3} - cos2 \pi }{tg \dfrac{13 \pi}{6} } }}$

• Sen 8π/3:

$\boxed{ \begin{array}{lr}\\ \large \sf \: sen \dfrac{8 \pi}{ 3} \\ \\\large \sf \: \dfrac{8.180}{3} = 480 \\ \\ \large \: \sf480 - 360 = 120 \\ \\\large \sf 180 - 120 = 60 \\ \\ \boxed{ \large\sf 60 = \dfrac{ \sqrt{3}}{2}} \\ \: \end{array}}$

• cos 2π:

$\boxed{ \large{ \sf \: cos \: 2 \pi = 1}}$

• tg 13π/3:

$\boxed{ \begin{array}{lr} \\ \large \sf \: tg \dfrac{13 \pi}{6} \\ \\\large \sf \: \dfrac{13.180}{6} = 390 \\ \\ \large \sf \:390 - 360 = 30 \\ \\ \boxed{\large \sf \dfrac{\sqrt{3}}{3}} \\ \: \end{array}}$

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• Cálculo da Expressão:

$\large \boxed{ \begin{array}{lr} \\ \large \sf \dfrac{sen \dfrac{8 \pi}{3} - cos2 \pi }{tg \dfrac{13 \pi}{6} } \: \\ \\ \large \sf \dfrac{ \dfrac{ \sqrt{3} }{2} - 1 }{ \dfrac{ \sqrt{3} }{3} } = \dfrac{3 - 2 \sqrt{3} }{2} \: \end{array}}$

➡️ Resposta:

• $\huge \boxed{ \boxed{ \huge \sf \dfrac{3 - 2 \sqrt{3} }{2} }}$