Question

f(x)= 5 + 4cos(x+100°), f(x)= 5​

Answer 1

Resposta: 5 - √6 + √2.

Explicação passo-a-passo:

A questão se dá justamente no exercício do cosseno da soma:

$[tex]f(x) = 5 + 4*cos(x + 100)\\\\f(5) = 5 + 4*cos(5 + 100)\\\\\f(5) = 5 + 4*cos(105)\\\\\f(5) = 5 + 4*cos(135 - 30 )\\\\\f(5) = 5 + 4*(cos(130)*cos(30)+sin(130)*sin(30))\\\\f(5) = 5 + 4*(-\frac{\sqrt{2} }{2}*\frac{\sqrt{3} }{2}+\frac{\sqrt{2} }{2}*\frac{1}{2})\\\\f(5) = 5 + 4*( -\frac{\sqrt{6} }{4}+\frac{\sqrt{2} }{4})\\\\\f(5) = 5+4* (-\frac{\sqrt{6} +\sqrt{2}}{4}  )\\\\(5) = 5 -\sqrt{6} +\sqrt{2}.$[/tex]