Transcript Document

4.4 Trigonometric Functions
of Any Angle

2
 
3
  
2
sin  
cos 
t an 
sin  
cos 
tan 
sin  
cos 
tan 
sin  
3
   2
cos 
2
t an 
0  

2
Find the sine, cosine, and tangent of  if (-3,4)
is a point on the terminal side of  .
Ex.
4
sin  
5
(-3,4)
? =5
4

-3
3
cos  
5
4
tan  
3
5
Ex. Given tan    and cos   0 , find
4
sin 
and
sec  .
First, determine what quadrant theta lies in.
Where is tan (-) and cos (+)?
IV
5
sin  
 .7809
41
4
-5
=?
 41
41
sec 
 1.6008
4
Reference Angles
A reference angle is the acute angle formed by the
terminal side of  and the horizontal axis.
Find the reference angles of 300o, 2.3, and –135o.
1.57
300o
2.3 rad
60o
3.14
3.14
-2.30
.84
45o
-135o
Evaluate the following.
tan (-210o)
1
30o
2
4
cos
3
240o
ref. angle
 3
2
3

3
 3
1
2
45o
-1
ref. angle
-1
1
 3
11
csc
4
3
 csc
4
60o
ref. angle
2
1

2
Find the cosine and tangent of theta if…..
1
sin  
3
1
3
? =2 2
and

 
2
2 2
cos  
3
1
2
tan 

4
2 2