# Calculator inverse tangent problem

## Homework Statement

Suppose that a wind is blowing from the direction N45ºW at a speed of 50 km/h. A pilot is steering a plane in the direction N60ºE at an airspeed of 250 km/h. Find the true course (direction) and ground speed (magnitude) of the plane.

## The Attempt at a Solution

The resultant vector will be in an upward direction in the second quadrant, right? I determined that the resultant vector
v = <25(√2) - 125(√3), 25(√2) + 125>

I am trying to find the angle that the plane is flying.
tan θ = [25(√2) + 125]/[25(√2) - 125(√3)]
Using inverse tangent and my calculator, I got an angle around -41.5 degrees.
If the resultant vector is in the second quadrant, this is wrong. I remember that the calculator sometimes will not work for inverse tangent, but I can't remember when, or what to do to fix it.

Use your trig identities. What is $\tan(\theta+180^\circ)$?