[size=150]Using the applet below, you can explore how sin, cos and tan are defined in the part of the unit circle that lies in [b]Quadrant I;[/b] as shown in the diagram below.[/size]

[size=150]The next applet shows sin, cos and tan values for angles in all four quadrants. Use the slider to change the angle [math]\alpha[/math]. [br][br][list][*]Sin [math]\alpha[/math] is the height of the right angle triangle and is represented by the blue segment. [br][/*][*]Cos  [math]\alpha[/math] is the base of the right angle triangle and is represented by the red segment. [/*][*]Tan [math]\alpha[/math] is the height of the brown segment where E is the intersection between the green ray and the tangent line at B.[/*][/list][/size]

[size=100][size=150]a. In which Quadrant do you find the SUPPLEMENTS of [b]Quadrant I [/b]angles?[br][/size][/size][size=150][br]b. Use the diagram above to explore the relationship between SIN, COS and TAN of supplementary angles in [b]Quadrant II [/b]and the related angle in [b]Quadrant I.[/b][br][br][/size][size=100][size=150]c. What rules can you write that connect SIN, COS and TAN of Quadrant I and III angles?[br][br]d. How would you [b]EXPLAIN[/b] why the relationships you have found between SIN, COS and TAN of angles in Quadrant I and Quadrant III make sense?[/size][/size]

[size=150]a. Use the applet to explore the relationship between SIN, COS and TAN of angles in [b]Quadrant III[/b] and angles in [b]Quadrant I[/b]. [br][br][b]Hint: [/b]for what pairs of angles in QI and QIII are the values equal or the negative of each other...[br][br]b. What rules can you write that connect SIN, COS and TAN of Quadrant I and III angles?[br][br]c. How would you [b]EXPLAIN[/b] why the relationships you have found between SIN, COS and TAN of angles in Quadrant I and Quadrant III make sense?[/size]

Using the same approach as above, investigate the relationships between SIN, COS and TAN of angles in [b]Quadrant IV[/b] and related angles in [b]Quadrant I.[/b]