Question

7. Calcule o valor das expressões abaixo: (1,5)
31
ig
1g
SET + sen
6
kime k
1-18
570
3
sensen
cos-+cos
4
13
1+cos 27

Answer 1

Resposta:

a) $n=-\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{2}$

b) $n=\frac{\sqrt{2}+1}{4}$

c) $n=-\frac{\sqrt{3}}{3}$

Explicação passo a passo:

a) $n=\frac{sen \left(\frac{\pi }{6}\right)+sen \left(\frac{\pi }{3}\right)}{sen \left(\pi \right)-sen \left(\frac{\pi }{4}\right)}$

$n=\frac{\frac{1}{2}+\frac{\sqrt{3}}{2}}{sen \left(\pi \right)-sen \left(\frac{\pi }{4}\right)}$

$n=\frac{\frac{1}{2}+\frac{\sqrt{3}}{2}}{-\frac{\sqrt{2}}{2}}$

$n=-\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{2}$

b) $n=\frac{cos \left(\frac{\pi }{4}\right)+cos \left(\frac{\pi }{3}\right)}{1+cos \left(2\pi \right)}$

$n=\frac{\frac{\sqrt{2}}{2}+\frac{1}{2}}{1+cos \left(2\pi \right)}$

$n=\frac{\frac{\sqrt{2}}{2}+\frac{1}{2}}{2}$

$n=\frac{\sqrt{2}+1}{4}$

c) $n=\frac{tg\left(\frac{3\pi }{4}\right)-tg \left(\frac{\pi }{6}\right)}{1-tg\left(\frac{5\pi }{3}\right)}$

$n=\frac{-1-\frac{\sqrt{3}}{3}}{1-tg \left(\frac{5\pi }{3}\right)}$

$n=\frac{-1-\frac{\sqrt{3}}{3}}{1+\sqrt{3}}$

$n=-\frac{\sqrt{3}}{3}$

Answer 2

Resposta:

a)

n = (sen(π/6) + sen(π/3))/(sen(π) - sen(π/4)

n = (1/2 + √3/2)/(0 - √2/2)

n = (-√3 - 1)/√2 = (-√6 - √2)/2

b)

n = (cos(π/4) + cos(π/3))/(1 + cos(2π)

n = (√2/2 + 1/2)/(1 + 1) = (1 + √2)/4

c)

n = (tg(3π/4) - tg(π/6))/(1 - tg(5π/3))

n = (-1 - √3/3)/(1 + √3)

n = (-1 - √3/3)*(1 - √3)/(-2)

n = (-1 + √3 - √3/3 + 1)/(-2)

n = (2√3/3)/-2 = -√3/3