In order to find the angle θ, in radians, whose tangent is [tex]-2[/tex] you have to follow those steps
Step 1
Using a calculator
Find the angle θ
[tex]Angle=arc\ tan(-2)= -63.43\°[/tex]
Remember that
the angle θ belong to the second quadrant
so
Angle θ=[tex]180\°-63.43\°=116.57\°[/tex]
Step 2
Convert degrees to radians
we know that
[tex]\pi\ radians=180\°[/tex]
[tex]116.57\°=116.57\°*\pi/180\°=0.648\pi\ radians[/tex]
therefore
the answer is
the angle θ is [tex]0.648\pi\ radians[/tex]
