An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 mi/hr. Find the rate at which the angle of elevation is changing when the angle is 30 degrees.
I found the answer to be 60 radians/hr by taking the derivative of the tangent function, which is the one that makes the most sense with the information you're given, and I know that answer is correct, but I first tried to find it by taking the derivative of sine or cosine, and I couldn't get the correct answer. I checked and re-checked my work, and can't figure out why it didn't work. Is there some reason that only one trig function would work to solve a specific problem?
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