3. Parameterize the curve r(t) = (2+ cos 3t, 3 – sin 3t, 4t) using arc length, s,
as a parameter. Use t = 0 as the reference point.
A point starts at (x, y) = (6, 0) and moves CCW along a circular path centered at (x, y) = (0, 0). Imagine an angle with its vertex at the center of
the path that subtends the arc the point has traveled.
Which of the following formulas expresses the x-coordinate of the point in terms of 0?
ㅠ
○x = 6 cos (0+
0x
-)
Ox= 6 sin(0)
x =
= 6 cos
Ox= = 6 cos (0)
X = cos(0)
$(1)
A curve is given parametrically by
x = 3 + 9e tan acos 0,
where a is a constant in the interval (0, π/2) and is a real-valued parameter.
y = 4 + 9e tan asin 0.
In this example, we can consider the whole curve by allowing the intrinsic angle to take any real value. Find an expression for tan in
terms of 0 and a.
Now, find an expression for the arclength s in terms of and a, choosing a sign convention such that s is positive and setting for
convenience s→→0 as →∞0₁
Finally, combine the previous two results to find a relation between s and. From the form of this relation (and/or the original parametric
equations) what shape must the curve have? (Choose one)
OA circle
OA spiral
OA cycloid
ONone of the other options
OA straight line
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY