Question

Consider the vector a(t)=〈cost,sint〉 with components that depend on a real number t. As the number t varies, the components of a(t) change as well, depending on the functions that define them. Write the vectors a(0) and a(π) in component form. Show that the magnitude ∥a(t)∥ of vector a(t) remains constant for any real number t. As t varies, show that the terminal point of vector a(t) describes a circle centered at the origin of radius 1.  

Answer 1