Download Lesson 9.9 Introduction To Trigonometry

Lesson 9.9
Introduction To Trigonometry
Objective:
After studying this section, you will be able to
understand three basic trigonometric
relationships
This section presents the three basic
trigonometric ratios sine, cosine, and
tangent.
The concept of similar triangles and the
Pythagorean Theorem can be used to
develop trigonometry of right triangles
Consider the following 30-60-90
triangles
J
E
B
c=2
A
b= 3
k=6
f=4
a=1
C
D
e= 2 3
h=3
d=2
F
H
j =3 3
K
Compare the length of the leg opposite the
30 angle with the length of the hypotenuse
in each triangle.
a 1
ABC ,   0.5
c 2
h 3
d 2

HJK
,
  0.5
DEF ,   0.5
k 6
f 4
By using similar triangles, we can see that in every
30-60-90 triangle
leg opposite 30  1

hypotenuse
2
leg adjacent 30 
3

hypotenuse
2
leg opposite 30  1
3


leg adjacent 30 
3
3
Engineers and Scientist have found it convenient to
formalize these relationships by naming the ratios of
sides. You should memorize these three basic ratios.
leg opposite 30  1
sine  sin 

hypotenuse
2
leg adjacent 30 
3
cosine  cos 

hypotenuse
2
leg opposite 30  1
3
tangent  tan 


leg adjacent 30 
3
3
Example 1
Find:
a.
b.
cos A
tan B
B
c
5
C
12
A
Example 2
Find the three trigonometric ratios for angles A and B
B
5
3
C
4
A
Example 3
Triangle ABC is an isosceles triangle, find sin C
A
13
B
13
10
C
Example 4
Use the fact that tan 40 is approximately 0.8391 to find
the height of the tree to the nearest foot.
h
50 ft
40
Summary
Summarize in your own words how
to find the sin, cos, and tangent of a
30-60-90 triangle.
Homework:
Worksheet 9.9