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Vector differential calculus: velocity and acceleration

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Here is the problem as it is printed in the book (kreyszig: Advanced Engineering Mathematics. sec. 8.6. Problem 10):
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(Elliptical Orbit) Consider the motion r(t) = cos t i + 2sin t j. Find the points of maximum speed and acceleration. Find the tangential and normal acceleration.
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Here is where I am in the problem:
Velocity = r' = -sin t i + 2cos t j
acceleration=r" = -cos t i + -2sin t j
(where i represents the x vector component and j the y component).

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Solution Summary

The vector differential calculus for velocity and acceleration is provided. The solution provides a detailed and step-by-step explanation for the problem.

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Maximum speed is when the magnitude of velocity is greatest:
Speed =Square root (sin^2(t)+4cos^2(t))=square root(1+3cos^2(t))
So speed is maximum when cos(t) = 1 or -1.
Cost=1 or -1 when t is either ...

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