θ = arc tan ( h / x )
dθ / dx = [ arc tan ( h / x ) ]' = - h / ( x² + h² )
A right triangle has base x meters and height h meters, where h is constant and x changes with respect to time t, measured in seconds. The angle θ, measured in radians, is defined by tanθ=hx. Which of the following best describes the relationship between dθdt, the rate of change of θ with respect to time, and dxdt, the rate of change of x with respect to time?
dθ/dt=(−h/x^2+h^2)dx/dt radians per second
dθ/dt=(h/x^2+h^2)dx/dt radians per second
dθ/dt=(−h/x sqrt(x^2+h^2)dx/dt radians per second
dθ/dt=(h/x sqrt(x^2+h^2)dx/dt radians per second
2 answers
θ = arc tan ( h / x ) because tan θ = h / x
tan θ is not h x as you wrote
tan θ is not h x as you wrote