1/26/2015 1 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 A B C D F E H J K c = 2 b = 3 a = 1 f = 4 d = 2 e = j = h = 3 k = 6 3 2 3 3 Compare the length of the leg opposite the 30 angle with the length of the hypotenuse in each triangle. 5 . 0 2 1 , c a ABC 5 . 0 4 2 , f d DEF 5 . 0 6 3 , k h HJK By using similar triangles, we can see that in every 30-60-90 triangle 2 1 30 hypotenuse opposite leg 2 3 30 djacent hypotenuse a leg 3 3 3 1 30 djacent 30 opposite a leg leg Engineers and Scientist have found it convenient to formalize these relationships by naming the ratios of sides. You should memorize these three basic ratios. 2 1 30 sin sine hypotenuse opposite leg 2 3 30 djacent cos cosine hypotenuse a leg 3 3 3 1 30 djacent 30 opposite tan tangent a leg leg Example 1 Find: a. b. A cos B tan A C B 5 12 c
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Lesson 9.9 Introduction To Trigonometry...Trigonometric Ratios 6 Objective: After studying this section, you will be able to use trigonometric ratios to solve right triangles. 38 We
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1/26/2015
1
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
A
B
C D F
E
H
J
K
c = 2
b = 3
a = 1 f = 4 d = 2
e = j =
h = 3 k = 6
32 33
Compare the length of the leg opposite the
30 angle with the length of the hypotenuse
in each triangle.
5.02
1 , c
aABC 5.0
4
2 , f
dDEF 5.0
6
3 , k
hHJK
By using similar triangles, we can see that in every
30-60-90 triangle
2
1 30
hypotenuse
oppositeleg
2
3 30djacent
hypotenuse
aleg
3
3
3
1
30djacent
30 opposite
aleg
leg
Engineers and Scientist have found it convenient to
formalize these relationships by naming the ratios of
sides. You should memorize these three basic ratios.
2
1 30 sinsine
hypotenuse
oppositeleg
2
3 30djacent coscosine
hypotenuse
aleg
3
3
3
1
30djacent
30 opposite tantangent
aleg
leg
Example 1 Find:
a.
b.
Acos
Btan
A C
B
5
12
c
1/26/2015
2
Example 2
Find the three trigonometric ratios for angles A and B
A C
B
3
4
5
Example 3
Triangle ABC is an isosceles triangle, find sin C A
C B
13
10
13
Example 4
Use the fact that tan 40 is approximately 0.8391 to find
the height of the tree to the nearest foot.
50 ft
h
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
1/26/2015
1
Lesson 9.10 Trigonometric Ratios
Objective:
After studying this section, you will be able to use trigonometric ratios to solve right triangles.
We can solve other
triangles that are
not specifically
30-60-90 and
45-45-90.
We can use a table
with the ratios
already calculated.
Degrees Radian Measure Sin Cos Tan Degrees Radian Measure Sin Cos Tan