Question

qual o valor de sen π/12 • cos 23π/12?

Answer 1

Resposta:

1/4

Explicação passo-a-passo:

$senp + senq = 2sen\frac{p+q}{2}cos\frac{p-q}{q}\\\\sen\frac{\pi }{12}cos\frac{23\pi}{12}=\frac{1}{2}(senp+senq)\\\\\frac{p+q}{2}=\frac{\pi }{12}\\p+q=\frac{2\pi}{12}\\\\\frac{p-q}{2}=\frac{23\pi }{12}\\\\p-q=\frac{46\pi }{12}\\\\2p=\frac{2\pi}{12}+ \frac{46\pi}{12}=\frac{48\pi}{12}=4\pi\\\\p=2\pi\\\\q=\frac{2\pi }{12}-2\pi=\frac{\pi}{6}-2\pi=\frac{-11\pi}{6}\\\\sen\frac{\pi }{12}cos\frac{23\pi}{12}=\frac{1}{2}(sen2\pi+sen(\frac{-11\pi}{6}))=\frac{1}{2}(0-sen\frac{11\pi }{6})=$

$\frac{1}{2}(0+\frac{1}{2})=\frac{1}{4}$