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Solved: Derivatives Consider the following parametric
Chapter 8, Problem 46E(choose chapter or problem)
Consider the following parametric curves.
a. Determine dy/dx in terms of t and evaluate it at the given value of t.
b. Make a sketch of the curve showing the tangent line at the point corresponding to the given value of t.
\(x=3 \sin t,\ y=3 \cos t;\ t =\pi/2\)
Questions & Answers
QUESTION:
Consider the following parametric curves.
a. Determine dy/dx in terms of t and evaluate it at the given value of t.
b. Make a sketch of the curve showing the tangent line at the point corresponding to the given value of t.
\(x=3 \sin t,\ y=3 \cos t;\ t =\pi/2\)
ANSWER:Solution 46EStep 1:To obtain the derivative we need which we can also write asEvaluating andseparately, we get Putting the valuesand into evaluate , we get.Hence the value of is . at is which means the tangent at this point is a vertical line.