Question

A) sen π/3 x sen 3π/2 - sen 4π x sen 2π/3

LETRA A, B, C - 4

LETRA C E D DA 3° QUESTÃO
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Answer 1

Oie, tudo bom?

Como está escrito no enunciado, farei as questões que se pede.

3. c)

= cos(35π/3)

= cos(5π/3 + 2 . 5π)

= cos(5π/3)

= 1/2

d)

= cos(- 40π/3)

= cos(40π/3)

= cos(4π/3 + 2 . 6π)

= cos(4π/3)

= - 1/2

4. a)

= sin(0°) . sin(135°) + sin(30°) . sin(360°)

= 0 . √2/2 + 1/2 . 0

= 0 + 1/2 . 0

= 0 + 0

= 0

b)

= sin(π/3) . sin(3π/2) - sin(4π/3) . sin(2π/3)

= √3/2 . (- 1) - (- √3/2) . √3/2

= - √3/2 . 1 - (- √3/2) . √3/2

= - √3/2 - (- √3/2) . √3/2

= - √3/2 + √3/2 . √3/2

= - √3/2 + [√3√3]/[2 . 2]

= - √3/2 + 3/4

c)

= cos(π/6) . cos(5π/3) + cos(4π/3) . cos(5π/6)

= √3/2 . 1/2 - 1/2 . (- √3/2)

= [√3 . 1]/[2 . 2] - 1/2 . (- √3/2)

= √3/4 - 1/2 . (- √3/2)

= √3/4 + 1/2 . √3/2

= √3/4 + [1√3]/[2 . 2]

= √3/4 + √3/4

= [√3 + √3]/4

= 2√3/4

= √3/2

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