Unit Circle and the Trigonometric Functions sin(x), cos(x) and tan(x)
Using the unit circle, you will be able to explore and gain deep understanding of some of the properties, such as domain, range, asymptotes (if any) of the trigonometric functions.
The relationships between the graphs (in rectangular coordinates) of sin(x), cos(x) and tan(x) and the coordinates of a point on a unit circle are explored using an applet.
1- Let x be a real number and P(x) a point on a unit circle such that the angle in standard position whose terminal side is segment OP is equal to x radians.(O is the origin of the system of axis used).
2- We define sin(x) as the y-coordinate of point P(x) on the unit circle.
3- We define cos(x) as the x-coordinate of a point P(x) on the unit circle.
4- We define tan(x) as the ratio of the y-coordinate and x-coordinate of point P(x) on a unit circle.
Interactive Tutorial Using Applets
Two possibilities to explore trigonometric function using the unit circle.
1) Using a Unit Circle HTML5 Applet
A java applet below
More references on unit circle and trigonometric functions.