# Related Rate Problem (Involving Trig.)

1. May 14, 2013

### NATURE.M

1. The problem statement, all variables and given/known data

A rocket is moving into the air with a height function given by h(t) = 200t^2. A camera located 150 m away from the launch site is filming the launch. How fast must the angle of the camera be changing with respect to the horizontal 4 seconds after liftoff?

2. Relevant equations

3. The attempt at a solution

If we create a diagram, we will see that
tan(θ)=(200t^2)/150 or (4t^2)/3

Differentiating with respect to t,

sec^2(θ)dθ/dt=8t/3 which becomes dθ/dt=8t/3 * cos^2(θ)

At t=4s, tan(θ)=64/3, and then by sinθ=cosθtanθ, we know sinθ=(64/3)cosθ

Then by sin^2(θ)+cos^2(θ)=1, we know that cos^2(θ)=9/4105

I would just like to know if all my steps are accurate, and if my final answer is correct, or if I made an error along the way, leading to an incorrect result?

2. May 14, 2013

### LCKurtz

Looks OK to me. You could have saved a couple of calculations by using $\sec^2\theta=1+\tan^2\theta$ instead of messing with the sines and cosines.

3. May 15, 2013

### NATURE.M

Okay thanks, and I completely forgot about that identity when doing this problem.