Question

seja tg=2, com 0<x<pi/2. calcule as demais razões trigonométricas de x​

Answer 1

Todas as funções trigonométricas que pertencem ao primeiro quadrante tem valores positivos.

$\mathsf{{\sec}^{2}(x)=1+{\tan}^{2}(x)}\\\mathsf{{\sec}^{2}(x)=1+{2}^{2}}\\\mathsf{{\sec}^{2}(x)=5}$

$\boxed{\boxed{\mathsf{\sec(x)=\sqrt{5}}}}$

$\mathsf{\cos(x)=\dfrac{1}{\sec(x)}}\\\mathsf{\cos(x)=\dfrac{1}{\sqrt{5}}}$

$\boxed{\boxed{\mathsf{\cos(x)=\dfrac{\sqrt{5}}{5}}}}$

$\mathsf{\sin(x)=\cos(x).\tan(x)}\\\mathsf{\sin(x)=\dfrac{\sqrt{5}}{5}.2}$

$\boxed{\boxed{\mathsf{\sin(x)=\dfrac{2\sqrt{5}}{5}}}}$

$\mathsf{\csc(x)=\dfrac{1}{\sin(x)}} \\\mathsf{\csc(x)=\dfrac{5}{2\sqrt{5}}}\\\mathsf{\csc(x)=\dfrac{5\sqrt{5}}{2.5}}$

$\boxed{\boxed{\mathsf{\csc(x)=\dfrac{\sqrt{5}}{2}}}}$

$\boxed{\boxed{\mathsf{\cot(x)=\dfrac{1}{\tan(x)}=\dfrac{1}{2}}}}$