Lissajous curves Consider the following Lissajous curves.

Chapter 8, Problem 77E

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QUESTION:

Consider the following Lissajous curves. Find all points on the curve at which there is (a) a horizontal tangent line and (b) a vertical tangent line. (See the Guided Projects for more on Lissajous curves.)

x = sin 2t, y = 2 sin t;

\(0\ \leq\ t\ \leq\ 2\pi\)

Questions & Answers

QUESTION:

Consider the following Lissajous curves. Find all points on the curve at which there is (a) a horizontal tangent line and (b) a vertical tangent line. (See the Guided Projects for more on Lissajous curves.)

x = sin 2t, y = 2 sin t;

\(0\ \leq\ t\ \leq\ 2\pi\)

ANSWER:

Solution 77E

Step 1:

We have to find all points on the curve at which there is

(a) a horizontal tangent line and

(b) a vertical tangent line.

A parametric curve has a horizontal tangent line when  

A parametric curve has a vertical tangent line when  

Given     x = sin2t, y = 2 sin t;      0 ≤ t ≤ 2π

x = sin2t, y = 2 sin t; 0 ≤ t ≤ 2π

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