Download 0 90 sin(90 ) θ- = 2) cos(90 ) θ- = 3

Section 5.4: Right Triangle Trigonometry
Right triangle:
0    90
Acute angle:
Ex: Given
Find the exact values of all Trig. Functions.
2
4
Complementary Angles: ( Cofunctions )
Two acute angles are called complementary if their sum is a right angle.
sin  
cos  
c
b
a
Ex:
sin(90   ) 

2) cos(90   ) 

3) tan(90   ) 

4) csc(90   ) 
1)
Ex: 1)
sin 65 
2)
tan

12

Reference Angle: Is the acute angle
terminal side  and the x  axis
R
(always taken positive) between the
Ex: Find the reference angles for the following angles.

1) 135 , 2)

7
11
13

, 3) 310 , 4)
, 5)
6
9
8
___________________________________________________________________
Ex: Find the exact values of
2
11
) , 4) tan(
)
3
6


2 
2

, 6) 1  tan 5  csc 85
5) tan12  cot 78




7) cos35 sin 55  sin 35 cos55
tan 2 40
1
tan 2 20 sin 70
8)

, 9)
2
2


cot 50
cos 50
sec 20
1)
cos 210 , 2) csc 300 , 3) sin(
___________________________________________________________________
Ex: If
1)
cot   2 , find the exact values of

tan  , 2) csc 2  , 3) tan(   ) , 4) sec 2 
2
Ex: Answer True or False
13

cos(
)  cos( ) ,
7
7
4

11
7
)   tan( ) , 4) sec(
)  sec( )
3) tan(
5
5
18
18
1)
sin(
7

)  sin(  ) ,
8
8
2)
___________________________________________________________________
_
Ex: Evaluate the followings
15
3
7
tan 2 (
)  csc 2 ( )  sin 2 ( )
8
8
6
4

11
2
)  cos 2 (  )  cos 2 (
)
2) cot ( 
3
9
18
1)