Final answer:
To find two unit vectors tangent to a curve defined by a vector-valued function, take the derivative of the function and then normalize the resulting vector.
Step-by-step explanation:
The two unit vectors that are tangent to the curve defined by the vector-valued function can be found by taking the derivative of the function and then normalizing the resulting vector.
Let's say the vector-valued function is r(t) = ⟨x(t), y(t)⟩.
1. Find the derivative of the function: r'(t) = ⟨x'(t), y'(t)⟩.
2. Normalize the derivative vector to get the tangent vector: T(t) = r'(t)/‖r'(t)‖, where ‖r'(t)‖ is the magnitude of r'(t).
By following these steps, you will obtain two unit vectors that are tangent to the curve at any given point.