?Consider the vector a(t) = ? cos t, sin t ? with components that depend on a real
Chapter 2, Problem 21(choose chapter or problem)
Consider the vector a(t) = 〈 cos t, sin t 〉 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.
a. Write the vectors a(0) and \(a(\pi)\) in component form.
b. Show that the magnitude ‖ a(t) ‖ of vector a(t) remains constant for any real number t.
c. As t varies, show that the terminal point of vector a(t) describes a circle centered at the origin of radius 1.
Text Transcription:
a(pi)
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