Question

Calcule o cosseno de um arco do primero quadrante , tal que ele seja o triplo do seno do mesmo arco​

Answer 1

$\mathsf{cos(x)=3sen(x)}\\\mathsf{sen^2(x)+cos^2(x)=1}\\\mathsf{sen^2(x)+(3sen(x))^2=1}\\\mathsf{sen^2(x)+9sen^2(x)=1}$

$\mathsf{10sen^2(x)=1}\\\mathsf{sen^2(x)=\dfrac{1}{10}}\\\mathsf{sen(x)=\sqrt{\dfrac{1}{10}}=\dfrac{1}{\sqrt{10}}=\dfrac{\sqrt{10}}{10}}$

$\boxed{\boxed{\boxed{\mathsf{cos(x)=\dfrac{3\sqrt{10}}{10}}}}}$