Question

O valor da Expressão E= arc cos 1/2 + arc sen + arc cos √2/2 pra hoje por favor !!!!

Answer 1

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$\sf arc~cos\bigg(\dfrac{1}{2}\bigg)=a\implies cos(a)=\dfrac{1}{2}\\\sf a=\dfrac{\pi}{3}\\\sf arc~sen(1)=b\implies sen(b)=1\\\sf b=\dfrac{\pi}{2}\\\sf arc~cos\bigg(\dfrac{\sqrt{2}}{2}\bigg)=c\implies cos(c)=\dfrac{\sqrt{2}}{2}\\\sf c=\dfrac{\pi}{4}$

$\sf E=arc~cos\bigg(\dfrac{1}{2}\bigg)+arc~sen(1)+arc~cos\bigg(\dfrac{\sqrt{2}}{2}\bigg)\\\sf E=a+b+c\\\sf E=\dfrac{\pi}{3}+\dfrac{\pi}{2}+\dfrac{\pi}{4}\\\sf E=\dfrac{4\pi}{12}+\dfrac{6\pi}{12}+\dfrac{3\pi}{12}\\\huge\boxed{\boxed{\boxed{\boxed{\sf E=\dfrac{13\pi}{12}}}}}\blue{\checkmark}$