1. Section 4.2 Trigonometric Functions: The Unit Circle

2. What you should learn:
• Identify a unit circle and describe its relationship to real numbers.
• Evaluate trigonometric functions using the unit circle.
• Use the domain and period to evaluate sine and cosine functions.
• Use a calculator to evaluate trigonometric functions.

3. Unit Circle

5. Definitions of Trigonometric Functions
Let t be a real number and let (x, y) be a point on the unit circle corresponding to t.
sin t = y
cos t = x
tan t = y/x, x ≠ o
cot t = x/y, y ≠ o
sec t = 1/x, x ≠ o
csc t = 1/y, y ≠ o

6. Example 1: Evaluating Trigonometric Functions.

7. Example 2: Evaluating Trigonometric Functions.
Evaluate the six trigonometric functions for

8. Domain and Period of Sine and Cosine
The domain of the sine and cosine functions is the set of real numbers. The range of the functions is from -1 to 1.

9. Definition of Periodic Function
A function f is periodic if there exists a positive real number c such that
f( t + c) = f(t)
for all t in the domain of f.

10. Odd Functions Even Functions
cos (-t) = cos (t)
sec (-t) = sec (t)
sin (-t) = -sin (t)
tan (-t) = -tan (t)
csc (-t) = -csc (t)
cot (-t) = -cot (t)

12. Evaluating Trigonometric Functions with a Calculator (Mode -> Radians)