1. Trig Functions of Real Numbers
Lesson 2.4a

2. The Unit Circle Consider a circle with radius r = 1
Wrap t onto the circumference
Then w(t) is a function which wraps t to a point P(x, y)
Also, t translates to θ (radians)
P(x, y) • t θ
r = 1

3. The Unit Circle The trig ratios for θ can tell us x and y Since r = 1
P(x, y) • θ
r = 1
View Spreadsheet Demo

4. Example Given Then What if What are sin, cos, tan? Determine P(x, y)
What are the trig functions? x y

5. Implications
It is now possible to take functions of angles greater than 360 (2π) or less than -360 (-2π)
Try these
Use both
Wrapping concept
Calculator (watch angle mode)

6. Properties of Trig Functions
Odd functions
f(-x) = - f(x)
Even functions
f(-x) = f(x)
Which of the trig functions are?? Odd Even
This definition is also applied to non trig functions.

7. Trig Functions are Periodic
The functions repeat themselves
The period is the smallest value, p for which f(x) = f(x + p)
For sin, cos, sec, csc
The period is 2π
For tan and ctn
The period is π

8. Assignment
Lesson 2.4a
Page 166
Exercises 1 – 47 odd