Question

(2.1) A curve is defined by the parametric equations \[ x=\cos 2 \theta . \quad y=2 \sin ^{3} \theta . \quad 0 \leq \theta \leq 2 \pi \] (a) Find an equation of the normal to the curve at the point where \( \theta=\frac{\pi}{6} \). (b) Find the Cartesian equation of the curve. [5] [5]

          (2.1) A curve is defined by the parametric equations
\[
x=\cos 2 \theta . \quad y=2 \sin ^{3} \theta . \quad 0 \leq \theta \leq 2 \pi
\]
(a) Find an equation of the normal to the curve at the point where \( \theta=\frac{\pi}{6} \).
(b) Find the Cartesian equation of the curve.
[5]
[5]

(2.1) A curve is defined by the parametric equations

x=cos 2 θ . y=2 sin ^3θ . 0 ≤θ≤ 2 π

(a) Find an equation of the normal to the curve at the point where θ=(π)/(6).
(b) Find the Cartesian equation of the curve.
[5]
[5]

Added by Martin T.

Engineering Mathematics

K. A. Stroud, Dexter J. Booth 5th Edition

Chapter 20

Instant Answer

Solved by Expert Brittany Stefanilo

Step 1

- \(x = \cos(2 \times \frac{\pi}{6}) = \cos\left(\frac{\pi}{3}\right) = \frac{1}{2}\). - \(y = 2 \sin^3\left(\frac{\pi}{6}\right) = 2 \left(\frac{1}{2}\right)^3 = \frac{1}{4}\). Show more…

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(2.1) A curve is defined by the parametric equations \[ x=\cos 2 \theta . \quad y=2 \sin ^{3} \theta . \quad 0 \leq \theta \leq 2 \pi \] (a) Find an equation of the normal to the curve at the point where \( \theta=\frac{\pi}{6} \). (b) Find the Cartesian equation of the curve. [5] [5]