Question

Trigonometria - Calcule as expressões

Answer 1

Explicação passo-a-passo:

a )

$cos \dfrac{\pi}{3} + cos \dfrac{\pi}{4} - cos2\pi$

$\dfrac{1}{2} + \dfrac{ \sqrt{2} }{2} - 1$

$- \dfrac{1}{2} + \dfrac{ \sqrt{2} }{2}$

$\red{ \dfrac{ - 1 + \sqrt{2} }{2} }$

b )

$2cos \dfrac{\pi}{6} + \dfrac{1}{2} cos \dfrac{7\pi}{4}$

$2 \times \dfrac{ \sqrt{3} }{2} + \dfrac{1}{2} \times \dfrac{ \sqrt{2} }{2}$

$\red{ \sqrt{3} + \dfrac{ \sqrt{2} }{4} }$

c )

$3cos \dfrac{\pi}{2} - 2cos \dfrac{5\pi}{4} + \dfrac{1}{2} cos\pi$

$3 \times 0 - 2 \times ( - \dfrac{ \sqrt{2} }{2} ) + \dfrac{1}{2} \times ( - 1)$

$0 + \sqrt{2} - \dfrac{1}{2}$

$\red{ \sqrt{2} - \dfrac{1}{2} }$

d )

$- \dfrac{2}{3} cos \dfrac{3\pi}{2} + \dfrac{3}{5} cos \dfrac{5\pi}{3} - \dfrac{6}{7} cos \dfrac{7\pi}{6}$

$- \dfrac{2}{3} \times 0 + \dfrac{3}{5} \times \dfrac{1}{2} - \dfrac{6}{7} \times ( - \dfrac{ \sqrt{3} }{2} )$

$0 + \dfrac{3}{10} + \dfrac{3}{7} \times \sqrt{3}$

$\red{ \dfrac{3}{10} + \dfrac{3 \sqrt{3} }{7} }$

Espero ter ajudado !!!