Answer:
length of the curve = 8
Step-by-step explanation:
Given parametric equations are x = t + sin(t) and y = cos(t) and given interval is
−π ≤ t ≤ π
Given data the arrow the direction in which the curve is traces means
the length of the curve of the given parametric equations.
The formula of length of the curve is
Given limits values are −π ≤ t ≤ π
x = t + sin(t) ...….. (1)
y = cos(t).......(2)
differentiating equation (1) with respective to 'x'
differentiating equation (2) with respective to 'y'
The length of curve is
on simplification , we get
here using sin^2(t) +cos^2(t) =1 and after simplification , we get
again using formula, 1+cost = 2cos^2(t/2)
Taking common we get ,
length of curve =
length of the curve is = 4(1+1) = 8
<u>conclusion</u>:-
The arrow of the direction or the length of curve = 8
