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.
Definitions
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 ycoordinate of point P(x) on the unit circle.
3 We define cos(x) as the xcoordinate of a point P(x) on the unit circle.
4 We define tan(x) as the ratio of the ycoordinate and xcoordinate 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
or
A java applet below
 Is there a point P(x) that cannot have any values for its x or ycoordinates? The x and ycoordinates are cos(x) and sin(x), what is the domain of sin(x), what is the domain of cos(x)?
answer
 Explore the xintercepts, the maximums and minimums (if any) of
the graphs of sin(x) and cos(x) using the unit circle.
answer
 Using the unit circle, do you think that any of the coordinates of a point on the circle can be larger than 1 or smaller than 1. Why do you think that sin(x) and cos(x) cannot be larger than 1 or smaller than 1?
answer
 Explore the periodicity of sin(x), cos(x) and tan(x).
answer
 tan(x)is the ratio ycoordinate / xcoordinate and whenever the xcoordinate of point P(x) is equal to zero, we cannot define tan(x).Find these points for x between zero and 2Pi. What is the domain of tan(x)?
answer
 At these same points where tan(x)is undefined, the graph of tan(x) on the right shows an asymptotic behavior, Explain. What do you think is the range of tan(x)? Find all xintercepts of tan(x) between 0 and 2Pi (inclusive). Explain their positions on the xaxis.
answer
More references on unit circle and trigonometric functions.
http://analyzemath.com/unitcircle/unit_circle_video_1.html
