Transcript 5.2 Trigonometric Ratios in Right Triangles

5.2 Trigonometric Ratios in Right Triangles
A triangle in which one angle is a right
angle is called a right triangle. The side
opposite the right angle is called the
hypotenuse, and the remaining two sides
are called the legs of the triangle.
c
b

90
a

Initial side
The six ratios of a right triangle are called
trigonometric functions of acute angles
and are defined as follows:
Function name Abbreviation
Value
sin 
sine of 
cos
cosine of 
tan 
tangent of 
cosecant of 
csc 
secant of 
sec 
cotangent of 
cot 
Opposite b
Adjacent a
sin  
 cos 

Hypotenuse c
Hypotenuse c
Opposite b
Hypotenuse c
tan  

csc 

Adjacent a
Opposite b
Hypotenuse c
Adjacent a
sec 
 cot  

Adjacent a
Opposite b
Find the value of each of the six
trigonometric functions of the angle
.
c = Hypotenuse = 13
12
13

Adjacent
b = Opposite = 12
a b  c
2
2
2
a  12  13
2
2
2
a  169  144  25
a 5
2
a  Adjacent = 5
b  Opposite = 12
c  Hypotenuse = 13
Opposite 12
Hypotenuse 13
sin 

csc 

Hypotenuse 13
Opposite 12
Hypotenuse 13
Adjacent
5
sec 

cos 

Adacent
5
Hypotenuse 13
Opposite 12 cot   Adjacent  5
tan 

Opposite 12
Adjacent 5
Reciprocal Identities
1
csc 
sin 
1
sec 
cos
1
cot  
tan 
FIND THE VALUE OF THE
RECIPROCAL FUNCTION:
1.
sin s = 3/5
2.
cos s = 4/5
3.
cot s = - ½
Opposite
12
Opposite
12
tan



tan Adjacent  5
Adjacent 5
Let’s go over those
special right Triangles:

0

6
Or
30 degrees

4
Or
45 degrees

3
Or
60 degrees
Sin  Cos  Tan 