Solution Found!
Lissajous curves Consider the following Lissajous curves.
Chapter 8, Problem 77E(choose chapter or problem)
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