Explore how big and small trig ratios can become. What controls them?

1) Notice the angles given. What is the measure of the missing angle?
2) Notice the three trig ratios. What is particular about them? Make a hypothesis that explains the relationship between sin(45), cos(45), and tan(45). Why do you think that is?
3) Move point D up and down.
- How does the side length of e affect the given angle?
- What is the smallest angle possible?
- What is the largest angle possible?
4) Play around with points D and E.
- What is the largest possible value of sin(B)?
- What is the smallest possible value of sin(B)?
- What is the largest possible value of cos(B)?
- What is the smallest possible value of cos(B)?
- What is the largest possible value of tan(B)?
- What is the smallest possible value of tan(B)?