# Inverse Trig Function Problem

1. Nov 21, 2013

### imull

1. The problem statement, all variables and given/known data
A patrol car is 50 ft from a long warehouse. The revolving light on top of the car turns at a rate of 30 rotations per minute. How fast is the beam of light moving along the warehouse wall when the beam makes a 45° angle with the line perpendicular from the light to the wall?

2. Relevant equations

3. The attempt at a solution
First I started out by setting θ as a function of x : tanθ=(x/50)→θ=arctan(x/50). So when θ=45°, x=50ft. dθ/dt is 30(2∏)=60∏. So taking the derivative: dθ/dt=[(50)/(502+x2)]dx/dt. After substituting values, 60∏=(0.01)dx/dt→dx/dt=6000∏ ft/min. Is this right?

2. Nov 21, 2013

### Dick

Yes, it is right. But you didn't really need to go through the arctan stuff. Just differentiate both sides of 50tanθ=x.

Last edited: Nov 21, 2013
3. Nov 21, 2013

### imull

Okay, thank you. The reason that I did the arctan stuff was because we're doing arctan derivatives, so I figured my teacher would want me to do it that way.