Question

Determine a tg x sabendo que cos x= raiz de 3 por 4

Answer 1

$\cos(x)=\dfrac{\sqrt3}{4}\qquad\tan(x)=\ ?\\\\\\\tan^2(x)=\sec^2(x)-1\\\\\tan^2(x)=\dfrac{1}{\cos^2(x)}-1\\\\\\\tan^2(x)=\dfrac{1}{\left(\dfrac{\sqrt3}{4}\right)^2}-1\\\\\\\tan(x)=\pm\sqrt{\dfrac{1}{\left(\dfrac{3}{16}\right)^2}-1}\\\\\\\tan(x)=\pm\sqrt{\dfrac{16}{3}-1}\\\\\\\boxed{\tan(x)=\pm\sqrt{\dfrac{13}{3}}}$