Question

Find the angle θ, in radians, in the second quadrant whose tangent is -2.

Answer 1

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 $0.648\pi\ radians$