1. Trigonometric Functions:Unit Circle
Section 4.2
Trigonometric Functions:Unit Circle
The Unit Circle is a circle with a radius of 1: x2 + y2 = 1.
Definition of Trig Functions using the Unit Circle
sin t = y-coordinate cos t = x-coordinate
tan t = coordinates csc t = coordinate
sec t = coordinate cot t = coordinates

2. Ex 1: Evaluate the six trigonometric functions for
a. sin b. cos
c. tan d. csc
e. sec f. cot

3. Ex 2: Evaluate the six trigonometric functions for
a. sin b. cos
c. tan d. csc
e. sec f. cot

4. Ex 3: Evaluate the six trigonometric functions for
a. sin b. cos
c. tan d. csc
e. sec f. cot

5. Ex 4: Evaluate the six trigonometric functions for
a. sin π b. cos π
c. tan π d. csc π
e. sec π f. cot π

6. Consider the sine function and the cosine function.
What is the domain and what is the range of these?
The domain of the sine and cosine functions are
all real numbers.
The range of the sine and cosine functions are all
values [-1, 1].

7. What happens to the values of the sine and
cosine functions as the t values increase?
The function values begin to repeat.
This characteristic of sine and cosine is called
periodic. A function is periodic if its values
repeat at consistent intervals.

8. Def: A function f is periodic if there exists a
Def: 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.
The least value c for which f is periodic is called
the period of f.

9. Cosine and secant are even functions so:
cos (t) = cos (-t) and sec (t) = sec (-t).
The remainder of the trig functions are odd so:
- sin (t) = sin (-t)
- csc (t) = csc (-t)
- tan (t) = tan (-t)
- cot (t) = cot (-t)

10. To evaluate trig functions on a calculator be sure
that the calculator is set for the correct mode
(degrees or radians).
Example 5: Evaluate the following trigonometric
functions with a calculator.
a. sin b. cot 1.5
c. csc d. cos 356°

11. Suggested Assignment:
Section 4.2
pg 264 – 265
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