1. Trigonometric Functions: The Unit Circle
Section 4.2
Trigonometric Functions: The Unit Circle

2. Objective By following instructions students will be able to:
Identify a unit circle and its relationship to real numbers.
Evaluate trigonometric functions using the unit circle.
Use the domain and period to evaluate sine and cosine functions.
Evaluate trigonometric functions.

3. Unit Circle
Circumference:
Suppose radius=1
Then,

4. The Trigonometric Functions
Let t be a real number and let (x,y) be the point on the unit circle corresponding to t.

5. Unit Circle

6. Example 1: Evaluating Trigonometric Functions
a) b)
c) d)

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

8. Domain and Period of Sine and Cosine?
range
Range
Periodic
Repeated revolutions or functions that behave in a repetitive manner.

9. Example 3: Use the Period to Evaluate Sine and Cosine
a) b)

10. Trigonometric Functions
Even and Odd
Trigonometric Functions
The cosine and secant functions are even.
The sine, cosecant, tangent, and cotangent functions are odd.

11. Example 4: Using a Calculator
a) b)

12. Revisit Objective Did we…
Identify a unit circle and its relationship to real numbers?
Evaluate trigonometric functions using the unit circle?
Use the domain and period to evaluate sine and cosine functions?
Evaluate trigonometric functions?

13. Homework
Pg 300 #s 1-42 ALL