We will see in Chapter 2 that the models of many mechanical systems involve the sine function sin θ, which is nonlinear. Obtain three linear approximations of f (θ) = sin θ, one valid near θ = 0, one...

We will see in Chapter 2 that the models of many mechanical systems involve the sine function sin θ, which is nonlinear. Obtain three linear approximations of f (θ) = sin θ, one valid near θ = 0, one near θ = π/3 rad (60◦), and one near θ = 2π/3 rad (120◦).

We will see in Chapter 7 that the models of many fluid systems involve the square-root function
, which is nonlinear. Obtain a linear approximation of f (h) =
 valid near h = 9.