1. 4.2 Trigonometric Function: The Unit circle

2. The Unit Circle
A circle with radius of 1
Equation x2 + y2 = 1

3. The Unit Circle with Radian Measures

4. Do you remember 30º, 60º, 90º triangles?
Now they are really! Important

5. Do you remember 30º, 60º, 90º triangles?
Now they are really! Important
Even more important
Let 2a = 1

6. Do you remember 30º, 60º, 90º triangles?
Let 2a = 1

7. Do you remember 30º, 60º, 90º triangles?

8. Do you remember 45º, 45º, 90º triangles?
When the hypotenuse is 1
The legs are

9. Some common radian measurements
These are the Degree expressed in Radians

10. The Unit Circle: Radian Measures and Coordinates

11. The Six Trig functions

12. Why does the book use “t” for an angle?
Since Radian measurement are lengths of an arc of the unit circle, it is written as if the angle was on a number line.
Where the distance is “t’ from zero.
Later when we graph Trig functions it just works better.

13. Lets find the Trig functions if
Think where this angle is on the unit circle.

14. Find the Trig functions of
Think where this angle is on the unit circle.

15. How about

16. There are times when Tan or Cot does not exist.
At what angles would this happen?

17. There are times when Tan or Cot does not exist.

18. If think of the domain of the trig functions, there are some limits.
Look at the unit circle. If x goes with Cos, then what are the possible of Cos?
It is the same with
Sin?

19. Definition of a Periodic Function
A function “f” is periodic if there exist a positive real number “ c” such that
f(t + c) = f(t) for all values of “t”.
The smallest “c” is called the period.

20. Even Function ( Trig. ) Cos (- t) = Cos (t) and Sec( -t) = Sec (t)
Also
Sin(-t) = -sin (t) and Csc (-t) = - Csc (t)
Tan(-t) = -Tan (t) and Cot(-t) = - Cot (t)

21. Homework
Page
# 1, 5, 9, 13, 17,
21, 25, 29, 33,
37, 41, 45, 48,
52, 59, 68

22. Homework
Page
# 2, 8, 12, 16,
20, 24, 28, 32,
36, 40, 44, 49,
58, 61