Find the arc length x = 2 cos $\theta$ + cos 2$\theta$ + 1, y = 2 sin $\theta$ + sin 2$\theta$, for 0 $\le$ $\theta$$\le$ 2 $\pi$.
A) 12 units
B) 14 units
C) 16 units
D) 18 units
E) 10 units

Question

Quizplus · Accepted Answer

The arc length of a parametric curve is given by the integral of the square root of the sum of the squares of the derivatives of x and y with respect to $\theta$. Calculating these derivatives and integrating over the interval from 0 to 2$\pi$ gives an arc length of 16 units.

Find the Arc Length X = 2 Cos θ\thetaθ + Cos 2

Find the Arc Length X = 2 Cos $\theta$ + Cos 2