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

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

14. How about

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

16. There are times when TanƟ does not exist.

17. There are times when cotƟ 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. Even Function ( Trig. ) Cos (- Ɵ) = Cos (Ɵ) Sec( - Ɵ) = Sec (Ɵ)
Sin(- Ɵ) = -sin (Ɵ)
Csc (- Ɵ) = - Csc (Ɵ)
Tan(- Ɵ) = -Tan (Ɵ)
Cot(- Ɵ) = - Cot (Ɵ)