Transcript Section 4.2 Trigonometric Functions: The Unit Circle The length of the intercepted arc is t.

Section 4.2
Trigonometric Functions: The
Unit Circle
The length of the intercepted arc is t. This is also the radian
measure of the central angle. Thus, in a unit circle, the radian
measure of the central angle is equal to the length of the
intercepted arc. Both are given by the same real number t.
Example
Use the figure at right to find the trigonometric
functions at t.
1 3
P  ,

2
2


Domain and Range of Sine and
Cosine Functions
Example
Use the figure at right to find the trigonometric
functions at t.
 2 2
P 
,

2
2


Example
Find the value of each trigonometric function
 
cot   
 4
 
sec   
 4
Example
5
2 5
Given sin t =
and cos t=
find the value of
5
5
each of the four remaining trigonometric functions.
Example
1
3
Given sin t = and cos t=
find the value of
2
2
each of the four remaining trigonometric functions.
Example
10

Given that cos t=
and 0  t< , find the
10
2
value of sin t using a trigonometric identity.
Periodic Functions
Example
Find the value of each trigonometric function
9
a. cot
4
5
b. cos
2
3
c. sec 4
Using a Calculator to Evaluate Trigonometric Functions
Example
Use a calculator to find the value to four decimal places:
9
a. cot
4
5
b. cos
2
3
c. sec 4
d. csc 1.2
Find the exact value of the trigonometric function.
 3 
Do not use a calculator. sec  - 
 4 
(a)
(b)
(c)
(d)
1
2
3

2
1

2
 2
5
Find cot
6
(a)
(b)
(c)
(d)
3

2
1
2
 3
2