SOLUTION: Suppose we have a graph of parametric equations x=bsin(t), y=b(cos(t))^3 on where t is on [0,2pi]. A. Find the point(s) on the given graph where the slope of the tangent line is

Question 1039917: Suppose we have a graph of parametric equations x=bsin(t), y=b(cos(t))^3 on where t is on [0,2pi].
A. Find the point(s) on the given graph where the slope of the tangent line is 3/4. (Find t values not x,y values)
B. Determine the area, in terms of b, of the region enclosed by the graph.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
A. Find the point(s) on the given graph where the slope of the tangent line is 3/4. (Find t values not x,y values).
and
==> and after differentiating both x and y wrt t.
==> after division.
To find the point(s) on the graph where the slope of the tangent line is 3/4, let .
==> ==> ==> .
==> or .
==> or .
B. Determine the area, in terms of b, of the region enclosed by the graph.
To determine the area, first express y in terms of x.
,
==> ,
==>
==>
==>
==>
==> or .
Now for purpose of getting the area assume that b > 0. (The sense of the graph in this case is clockwise. b < 0 would only change the direction to ccw but would yield the same graph and the same area.)
==> Area =
(I wrote it this way rather than . They give the same answer.)
Let x = bsint.
==> dx = bcostdt
==> Area =
=
Using ,
Area =
=
=
=
=

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