Sine, cosine and tangent in a Unit Circle.
Quadrant I
Using the applet below, you can explore how sin, cos and tan are defined in the part of the unit circle that lies in Quadrant I; as shown in the diagram below.
The next applet shows sin, cos and tan values for angles in all four quadrants. Use the slider to change the angle .
- Sin is the height of the right angle triangle and is represented by the blue segment.
- Cos is the base of the right angle triangle and is represented by the red segment.
- Tan is the height of the brown segment where E is the intersection between the green ray and the tangent line at B.
Quadrants I and II
a. In which Quadrant do you find the SUPPLEMENTS of Quadrant I angles?
b. Use the diagram above to explore the relationship between SIN, COS and TAN of supplementary angles in Quadrant II and the related angle in Quadrant I.
c. What rules can you write that connect SIN, COS and TAN of Quadrant I and III angles?
d. How would you EXPLAIN why the relationships you have found between SIN, COS and TAN of angles in Quadrant I and Quadrant III make sense?
Quadrants I and III
a. Use the applet to explore the relationship between SIN, COS and TAN of angles in Quadrant III and angles in Quadrant I.
Hint: for what pairs of angles in QI and QIII are the values equal or the negative of each other...
b. What rules can you write that connect SIN, COS and TAN of Quadrant I and III angles?
c. How would you EXPLAIN why the relationships you have found between SIN, COS and TAN of angles in Quadrant I and Quadrant III make sense?
Quadrants I and IV
Using the same approach as above, investigate the relationships between SIN, COS and TAN of angles in Quadrant IV and related angles in Quadrant I.