Question

Let θ (in radians) be an acute angle in a right triangle, and let x and y, respectively, be the lengths of the sides adjacent and opposite θ. Suppose also that x and y vary with time. a. How are dθ/dt, dx/dt and dy/dt related? Please give steps and explain!

Answer 1

tan(theta(t))=y(t)/x(t)

differentiate
sec^2(theta(t))*theta'(t)=
y'(t)x(t)-y(t)x'(t)/x^2(t)
thus
theta'(t)=
(y'(t)x(t)-y(t)x'(t))
divided by (x^2(t)*sec^2(θ(t)) ....