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Parametric Curves: Example 2: Unit Circle

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First published at 00:19 UTC on February 20th, 2018.

Math Easy Solutions

MES

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In this video I go over another example on parametric curves and this time graph the curve formed by the parametric equations x = cos(t) and y = sin(t). Using the Pythagorean trig identity, sin^2(x) + cos^2(x) = 1, I show that in fact the curve defined by these parametric equations is a unit circle, which is a circle with a radius of 1. The circle is formed by starting at the point (1, 0) and then rotating around counterclockwise one full rotation. The parameter t, in this specific example represents the angle that is formed from the origin to a point on the unit circle. This is a very interesting video on how parametric equations define common shapes and curves that we are accustomed to, such as a circle. So make sure to watch this video!

Download the notes in my video:

Written Notes: https://1drv.ms/b/s!As32ynv0LoaIht5raiLJv4OemhkTgQ
Excel File: https://1drv.ms/x/s!As32ynv0LoaIht5s8piFIxyGub-LxA?e=WXEKBt

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-curves-example-2-unit-circle

Related Videos:

Parametric Curves: Example 1: https://youtu.be/0k7QyWa9-HA
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw .

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