Verify that each equation is an identity. tan u sin 2u = 2 - 2 cos2 u

Vector-Valued Functions Part 1 Saadiq Shaik September 2016 1 Introduction to Vector-Valued Functions A vector-valued function is function with a domain of real numbers and a range of vectors. This is in contrast to functions in prior calculus courses, which we will refer to as real-valued functions. Every VVF corresponds to 3 RVFs, referred to as component functions. F(t) = f (t)i + f (t)j + f (t)k 1 2 3 This can also be written in parametric form as x = f1(t);y = f2(t);z = 3 (t) Using the de▯nition of parametric equations given in the last chapter, we can write the VVF equation as F(t) = (x + at)i + (y + bt)