Question

How many angles are found in between 0 and 2π that satisfy the equation ItanxI = 5 ?

Answer 1

$|\tan(x)|=5$

This equation is equivalent to two equations:

$\tan(x)=5\;or\;\tan(x)=-5.$

Each of these equations has two solutions on the interval $[0,2\pi).$

Thus, the equation $|\tan(x)|=5$ has four solutions on the interval $[0,2\pi).$