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