Lesson 9 9 introduction to trigonometry
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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.

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Lesson 9.9 Introduction To Trigonometry

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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


Lesson 9 9 introduction to trigonometry

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


Lesson 9 9 introduction to trigonometry

Consider the following 30-60-90 triangles

Compare the length of the leg opposite the 30 angle with the length of the hypotenuse in each triangle.

J

E

B

k = 6

f = 4

h = 3

d = 2

c = 2

a = 1

A

H

D

C

F

K

e =

j =

b =


Lesson 9 9 introduction to trigonometry

By using similar triangles, we can see that in every 30-60-90 triangle


Lesson 9 9 introduction to trigonometry

Engineers and Scientist have found it convenient to formalize these relationships by naming the ratios of sides. You should memorize these three basic ratios.


Lesson 9 9 introduction to trigonometry

Example 1

Find:

a.

b.

B

c

5

C

A

12


Lesson 9 9 introduction to trigonometry

Example 2

Find the three trigonometric ratios for angles A and B

B

5

3

C

A

4


Lesson 9 9 introduction to trigonometry

Example 3

Triangle ABC is an isosceles triangle, find sin C

A

13

13

B

C

10


Lesson 9 9 introduction to trigonometry

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


Lesson 9 9 introduction to trigonometry

Summary

Summarize in your own words how to find the sin, cos, and tangent of a 30-60-90 triangle.

Homework:

Worksheet 9.9


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