Question

calcule o valor de A, sendo A= (sen 30° + cotg 45°) ao quadrado

Answer 1

Pra responder essa questão, precisamos lembrar da tabela de seno, cosseno e tangente dos arcos notáveis (anexo).

Assim, temos:

$A~=~\left(sen(30^\circ)~+~cotg(45^\circ)\right)^2\\\\\\A~=~\left(sen(30^\circ)~+~\dfrac{1}{tg(45^\circ)}\right)^2\\\\\\A~=~\left(\dfrac{1}{2}~+~\dfrac{1}{1}\right)^2\\\\\\A~=~\left(\dfrac{3}{2}\right)^2\\\\\\A~=~\dfrac{3^2}{2^2}\\\\\\\boxed{A~=~\dfrac{9}{4}}~~ou~~\boxed{A~=~2,25}$